Chow Group Research Articles

Zero-cycles on double EPW sextics

The Chow rings of hyperKähler varieties are conjectured to have a particularly rich structure. In this paper, we focus on the locally complete family of double EPW sextics and establish some properties of their Chow rings. First, we prove a Beauville–Voisin type theorem for zero-cycles on double EPW sextics; precisely, we show that the codimension-4 part of the subring of the Chow ring of a double EPW sextic generated by divisors, the Chern classes and codimension-2 cycles invariant under the anti-symplectic covering involution has rank one. Second, for double EPW sextics birational to the Hilbert square of a K3 surface, we show that the action of the anti-symplectic involution on the Chow group of zero-cycles commutes with the Fourier decomposition of Shen–Vial.

Two applications of the integral regulator

We review Li's refinement of the KLM regulator map, and use it to detect torsion phenomena in higher Chow groups.

Relationship between perirenal adipose tissue neuropeptide Y and insulin resistance in nutritional transition model

To observe the changes of neuropeptide Y(NPY) expression in perirenal adipose tissue and its relationship with insulin resistance in the nutritional transition models of refeeding after calorie restriction. SPF Male SD rats, aged 8 weeks, were randomly divided into normal chow group and refeeding with normal chow after calorie restriction for 4 weeks group. NPY gene expression in perirenal adipose tissue were detected by real-time quantitative PCR at the end of 4 and 12 weeks, along with fasting plasma glucose, fasting serum lisulin, free fatty acids and average glucose infusion rate(GIR_(60-120)) of hyperinsulinemic-euglycemic clamp test for 60-120 minutes. NPY gene mRNA expression in perirenal adipose tissue was detected by real-time quantitative PCR. And the relationship between NPY gene expression and insulin resistance was detected by Spearman correlation analysis. The expression level of NPY gene in perirenal adipose tissue in caloric restriction for 4 weeks group was significantly increased by calorie restriction(P<0. 01). After refeeding, the expression level of NPY gene in refeeding with normal group was still slightly increased, which was significantly higher than that in normal group at the end of the experiment(P<0. 01). The levels of fasting plasma glucose and fasting insulin in caloric restriction for 4 weeks group decreased slightly, GIR_(60-120) increased slightly, but there were no statistical differences compared with normal group(P>0. 05), but free fatty acid levels increased significantly(P<0. 01). After refeeding, the levels of fasting insulin, free fatty acid in refeeding with normal group increased significantly, GIR_(60-120) decreased evidently(P<0. 01), but the changes of fasting blood glucose were not obvious. The result of stepwise regression showed that the expression level of NPY gene in perirenal adipose tissue was closely related to GIR_(60-120) and fasting insulin, with R values of-0. 816 and 0. 789 respectively(R~2=0. 892, P<0. 01). The result of correlation analysis showed that in the 4-week group, the mRNA expression level of NPY gene in perirenal adipose tissue was closely related to GIR_( 60-120)、fasting insulin and free fatty acid, with R values of-0. 765, 0. 716 and 0. 657 respectively(P<0. 01). In the 12 week group, the mRNA expression level of NPY gene in perirenal adipose tissue was closely related to GIR_(60-120), fasting insulin and free fatty acid, with R values of-0. 853, 0. 622 and 0. 608 respectively(P<0. 01). The mRNA expression of NPY gene in perirenal adipose tissue was closely related to indicators of insulin resistance. It is an important factor affecting insulin sensitivity.

A moving lemma for relative 0-cycles

We prove a moving lemma for the additive and ordinary higher Chow groups of relative $0$-cycles of regular semi-local $k$-schemes essentially of finite type over an infinite perfect field. From this, we show that the cycle classes can be represented by cycles that possess certain finiteness, surjectivity, and smoothness properties. It plays a key role in showing that the crystalline cohomology of smooth varieties can be expressed in terms of algebraic cycles.

Rational equivalence and Lagrangian tori on K3 surfaces

Fix a symplectic K3 surface X homologically mirror to an algebraic K3 surface Y by an equivalence taking a graded Lagrangian torus L \subset X to the skyscraper sheaf of a point y \in Y . We show there are Lagrangian tori with vanishing Maslov class in X whose class in the Grothendieck group of the Fukaya category is not generated by Lagrangian spheres. This is mirror to a statement about the “Beauville–Voisin subring” in the Chow groups of Y , and fits into a conjectural relationship between Lagrangian cobordism and rational equivalence of algebraic cycles.

Effect of High Fructose Corn Sirup on Pancreatic Ductal Adenocarcinoma Induced by Dimethyl Benzantracene (DMBA) in Rats

Increased risk of pancreatic cancer may be associated with consumption of sugar containing foods. The aim of this study was to evaluate the effect of peach nectar containing high fructose corn sirup (HFCS) consumption in a pancreatic carcinogenesis rat model induced by 7,12-Dimethyl benzanthracene (DMBA). Fifty-day-old male Sprague Dawley rats were fed with peach nectar containing HFCS + chow, peach nectar containing sucrose + chow and only chow. After 8 mo, feeding period, each group was divided into two subgroups, in which the rats were implanted with DMBA and no DMBA (sham). Histologic specimens were evaluated according to the routine tissue processing protocol. The animals with ad libitum access to pn-HFCS, pn-sucrose and chow (only) showed significant differences in chow consumption and glucose level. Necropsy and histopathologic findings showed tumor formation in the entire group treated with DMBA. Excluding one rat in chow group, which was classified as poorly differentiated type, the others were classified as moderately differentiated pancreatic ductal adenocarcinoma (PDAC). This study demonstrated that daily intake of HFCS did not increase body weight and there was no effect of peach nectar consumption on the development of PDAC induced by DMBA in rats.

367-OR: High-Fat and Fructose Feeding Severely Impairs Hepatic Glucose Effectiveness

Diets high in fat and fructose (HFFD) disrupt glucose metabolism. The aim of this study was to determine if HFFD impairs hepatic glucose effectiveness (i.e., the ability of glucose per se to stimulate net hepatic glucose uptake [NHGU] and/or to suppress glucose production [Ra]). In overnight fasted dogs fed either a chow diet or HFFD for 1 month, somatostatin, 3-3H-glucose, and basal hepatic portal vein infusions of insulin and glucagon were given. After a basal sampling period, these infusions continued for 4h while glucose was infused to create a 3-fold rise in plasma glucose. Since hepatic glucose uptake is also stimulated by a negative arterial to portal vein glucose gradient, such as occurs with glucose ingestion, glucose was either all infused into a peripheral vein (Chow-PeG, n=6; HFFD-PeG, n=6), or a portion was also given into the portal vein (4 mg/kg/min; Chow-PoG, n=5; HFFD-PoG, n=5). There were no differences in plasma insulin, glucagon, arterial glucose, or hepatic glucose load between groups. In response to hyperglycemia, the liver switched from making (basal period) to storing (last h) glucose in the chow fed groups (1.1±0.1 to -2.0±0.5* mg/kg/min in Chow-PeG, and 1.3±0.1 to -3.0±0.9* in Chow-PoG; a negative rate indicates uptake). Conversely, HFFD markedly reduced liver glucose effectiveness. In fact, with HFFD the liver did not take up glucose in response to hyperglycemia whether the portal signal was absent (1.4±0.1 to 1.0±0.3 in HFFD-PeG) or present (1.6±0.3 to 0.0±0.3* in HFFD-PoG). Thus, in the Chow vs. HFFD groups, the impact of hyperglycemia on overall net hepatic glucose balance was 3.1±0.5 vs. 0.4±0.4* (13% of normal) in the absence of portal glucose delivery and 4.3±0.9 vs. 1.6±0.5* (37% of normal) in its presence. Hyperglycemia suppressed Ra by 75±12 vs. 22±6%* (last h) in Chow vs. HFFD-PeG, respectively, and by 81±14 vs. 34±7%* in Chow vs. HFFD-PoG. In summary, HFFD induced a severe impairment in hepatic glucose effectiveness but did not affect the liver’s response to the portal glucose signal. (*P<0.05). Disclosure D.S. Edgerton: None. G. Kraft: None. B. Farmer: None. M. Scott: None. M.S. Smith: None. A.D. Cherrington: Advisory Panel; Self; Biocon, Fractyl Laboratories, Inc., Metavention, Sekkei Bio, Sensulin, LLC., vTv Therapeutics, Zafgen, Inc. Consultant; Self; Thetis Pharmaceuticals LLC. Research Support; Self; Diasome Pharmaceuticals, Inc. Other Relationship; Self; Abvance Therapeutics, Novo Nordisk Inc. Funding National Institutes of Health (R01DK18243)

Birth Outcomes and Neuroapoptotic Markers in the Neonatal Brain Are Affected by Maternal Diet Qualities in Rats Exposed to Ethanol During Gestation

Abstract Objectives Women drinking ethanol (EtOH) during pregnancy may have children with fetal alcohol spectrum disorders (FASD) that vary in the severity of symptoms. This may be attributable to maternal nutritional status. This study examined two different maternal diet qualities, chow vs. formulated energy dense (E-dense) diet, on birth outcomes and neuroapoptotic markers in the neonatal brain of rats exposed to EtOH during gestation. Methods Female Sprague-Dawley rats were randomly assigned to four groups: chow (n = 6), chow + EtOH (n = 7) (20% v/v in drinking water), E-dense (n = 6), and E-dense + EtOH (n = 8). At postnatal day (PD) 7, representing brain growth spurt in rats, ceramides and caspase-3 activity (markers for apoptosis) in the cortex, cerebellum and hippocampus were measured using gas chromatography and a caspase-3 assay kit, respectively. Results Without EtOH exposure, dams fed E-dense diet had an approximately 5% higher body weights than dams fed chow. With EtOH exposure, dams fed E-dense diet had 2–5% less weight loss during gestation than dams fed chow (P < 0.05). EtOH consumption did not change the litter size in E-dense group, but decreased in chow group. Dams from E-dense groups had 2.1 times less neonatal deaths than dams from chow groups. At PD7, pups from E-dense groups had higher body weights regardless of EtOH consumption compared to pups from chow groups (P < 0.0001). EtOH increased ceramides in the hippocampus of pups from chow group, which was reduced by the E-dense diet (P < 0.05). No significant changes were found in caspase-3 activity. Conclusions The E-dense diet provided to dams attenuated EtOH-induced weight loss and ceramide elevations in the hippocampus of pups as compared with the chow diet. Ceramide elevations did not lead to changes in caspase-3 activity, which requires a further study to find whether other apoptotic markers preceding caspase-3 activation are stimulated. This study indicates that the quality of maternal diet impacts birth outcomes and neuroapoptotic markers in neonates with prenatal EtOH exposure, and maternal nutrition is a potential factor to reduce the severity of FASD. Funding Sources This work was supported by Research Manitoba, Canada-Israel International Fetal Alcohol Consortium and Manitoba Graduate Scholarship.

Sects

By explicitly describing a cellular decomposition we determine the Borel invariant cycles that generate the Chow groups of the quotient of a reductive group by a Levi subgroup. For illustration we consider the variety of polarizations SLn/S(GLp×GLq), and we introduce the notion of a sect for describing its cellular decomposition. In particular, for p=q, we show that the Bruhat order on the sect corresponding to the dense cell is isomorphic, as a poset, to the rook monoid with the Bruhat-Chevalley-Renner order.

Effects of Exercise Training on Vascular Inflammatory Markers in High-fat Diet-induced Obese Rats

OBJECTIVES The purpose of this study was to confirm the positive effects on the inflammatory expression and functional changes of blood vessels by aerobic exercise training and dietary control in high-fat diet induced obese rats.METHODS Forty 10-week-old male Wistar rats were treated with high-fat diet for 6 weeks, followed by 4 groups as sedentary + chow diet group (Chow), sedentary + high fat diet group (HFD), exercise + chow diet group (Chow-Ex), high fat diet + Exercise group (HFD-Ex) after obesity induction. After treadmill running exercise and dietary treatment were performed for 8 weeks, body composition, endurance performance and muscular endurance, blood glucose, CRP, NO, insulin, eNOS, iNOS, protein expression of IL-6 and TNF-α in aortic vascular tissues was analyzed.RESULTS High-fat diet intake leads to an increase in body weight and visceral fat, an increase in insulin resistance and an increase in inflammation factors. The blood NO level was significantly higher (p <0.05) in the HFD and Chow groups than in the non-exercise group. Blood insulin levels were significantly higher (p <0.05) in the HFD group without exercise than in all other groups. Blood eNOS activity was significantly higher (p <0.05) in the HFD and Chow groups than in the non-exercise group. The expression level of IL-6 protein in the vascular tissues was significantly higher (p <0.05) in the HFD group without exercise than the other groups. The expression level of TNF-α was significantly lower (p <0.05) in the HFD and Chow groups than in the non-exercise group.CONCLUSIONS The results of this study confirmed that exercise training through aerobic exercise and dietary control may help to reduce inflammatory expression and improve vascular endothelial function in high-fat diet induced obese rats.

On the integral Hodge conjecture for real varieties, I

We formulate the "real integral Hodge conjecture", a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally connected varieties. We relate it to the problem of determining the image of the Borel-Haefliger cycle class map for 1-cycles, with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the Chow group of 1-cycles of real threefolds. New results about these problems are obtained along the way.

DEFORMATION THEORY OF THE CHOW GROUP OF ZERO CYCLES

Abstract We study the deformations of the Chow group of zerocycles of the special fibre of a smooth scheme over a Henselian discrete valuation ring. Our main tools are Bloch’s formula and differential forms. As a corollary we get an algebraization theorem for thickened zero cycles previously obtained using idelic techniques. In the course of the proof we develop moving lemmata and Lefschetz theorems for cohomology groups with coefficients in differential forms.

On the arithmetic of weighted complete intersections of low degree

A variety is rationally connected if two general points can be joined by a rational curve. A higher version of this notion is rational simple connectedness, which requires suitable spaces of rational curves through two points to be rationally connected themselves. We prove that smooth, complex, weighted complete intersections of low enough degree are rationally simply connected. This result has strong arithmetic implications for weighted complete intersections defined over the function field of a smooth, complex curve. Namely, it implies that these varieties satisfy weak approximation at all places, that R-equivalence of rational points is trivial, and that the Chow group of zero cycles of degree zero is zero.

Endoplasmic reticulum stress in forebrain subfornical organ excitatory neurons during diet‐induced obesity

Endoplasmic reticulum (ER) stress and activation of the unfolded protein response (UPR) in the brain are emerging as key mechanisms in obesity‐related cardiovascular and metabolic diseases. For example, we recently demonstrated that inhibition of brain ER stress rescues hypertension and hepatic steatosis during high fat diet (HFD) feeding. Additional findings pointed to robust HFD‐induced ER stress in the subfornical organ (SFO), a circumventricular nucleus located outside of the blood‐brain‐barrier that is crucial for cardiometabolic regulation. The neuron population and anatomical location within the SFO that experiences ER stress during obesity remains unknown. Based on this, we comprehensively investigated UPR activation in the SFO during diet‐induced obesity. Six wk old male C57Bl/6J mice were placed on a HFD (n=4) or remained on normal chow (n=5) for 11 wks. Using serial cryosections, immunohistochemistry revealed marked upregulation of the ER chaperone glucose‐regulated peptide 78 kDa (GRP78) in the SFO of HFD fed mice, relative to normal chow controls (positive cells/section: 102±8 vs 177±9, normal chow vs HFD, p<0.05). This was evident throughout the rostral to caudal extent of the SFO (fold normal chow: rostral, 1.4±0.2; medial, 1.8±0.2; caudal, 1.8±0.1; all p<0.05). Similar findings were obtained when examining the ER chaperone protein disulfide isomerase (e.g. positive cells/section: 75±8 vs 107±4, normal chow vs HFD, p<0.05). Accumulating evidence indicates involvement of the PERK‐eIF2α pathway (protein kinase R like endoplasmic reticulum kinase‐eukaryotic initiation factor 2α) in cardiometabolic diseases and in line with this, the number of PERK expressing cells (cells/section: 32±10 vs 89±5, normal chow vs HFD, p<0.05) and downstream phosphorylated eIF2α positive cells (cells/section: 51±12 vs 125±24, normal chow vs HFD, p<0.05) was markedly elevated in the SFO following HFD feeding. The SFO can be anatomically subdivided into “core” and “shell” zones, which have distinct efferent projections to downstream nuclei involved in fluid, cardiovascular, and energy homeostasis; UPR activation was evident in both the core and shell zones. Given that a significant portion of SFO neurons that project to cardiometabolic nuclei are glutamatergic, we next investigated HFD‐induced ER stress in excitatory SFO neurons using double immunohistochemistry for UPR markers and the neuronal indicator calcium/calmodulin‐dependent kinase II (CAMKII; n=7/group). While the number of CAMKII positive neurons in the SFO was similar between HFD and normal chow groups, UPR activation was clearly evident in excitatory neurons during obesity as indicated by increased co‐localization of CAMKII with GRP78 (46+2 vs 59+3%, normal chow vs HFD, p<0.05), PDI (30+1 vs 49+3%, normal chow vs HFD, p<0.05), and phosphorylated eIF2α (40+2 vs 55+3%, normal chow vs HFD, p<0.05). Collectively, these findings indicate that obesity is associated with widespread anatomical ER stress throughout the SFO, including within excitatory neurons – suggesting that SFO ER stress during obesity has the potential to influence diverse downstream nuclei and thus physiological processes.Support or Funding Information1R01DK117007, 1R01HL141393

The Modularity of Special Cycles on Orthogonal Shimura Varieties over Totally Real Fields under the Beilinson–Bloch Conjecture

AbstractWe study special cycles on a Shimura variety of orthogonal type over a totally real field of degree d associated with a quadratic form in $n+2$ variables whose signature is $(n,2)$ at e real places and $(n+2,0)$ at the remaining $d-e$ real places for $1\leq e <d$. Recently, these cycles were constructed by Kudla and Rosu–Yott, and they proved that the generating series of special cycles in the cohomology group is a Hilbert-Siegel modular form of half integral weight. We prove that, assuming the Beilinson–Bloch conjecture on the injectivity of the higher Abel–Jacobi map, the generating series of special cycles of codimension er in the Chow group is a Hilbert–Siegel modular form of genus r and weight $1+n/2$. Our result is a generalization of Kudla’s modularity conjecture, solved by Yuan–Zhang–Zhang unconditionally when $e=1$.

Hypothalamic glial cells isolated by MACS reveal that microglia and astrocytes induce hypothalamic inflammation via different processes under high-fat diet conditions

Glial cells can mediate hypothalamic inflammatory processes induced in response to a high-fat diet (HFD). We used magnetic-activated cell sorting (MACS) to isolate microglia and astrocytes from hypothalamus of mice fed HFD and examined changes in expression of inflammation-related cytokines and markers related to glial cell activation status.Hypothalamus from male C57BL6 mice fed a chow diet (chow) or HFD for 1, 3, or 28 days were collected and microglia and astrocytes were isolated by MACS. After confirming cell viability by fluorescence activated cell sorting, mRNA expression levels of inflammation-related cytokines and markers of glial cell activation status were examined by qRT-PCR, which revealed that both glial cell types isolated by MACS retained specificity.On day 3 of HFD, both CD86 and TNFα mRNA expression was significantly increased in microglia relative to the chow group. In astrocytes, TNFα mRNA expression levels were similar between the chow and HFD groups on day 3, but anti-inflammatory cytokine IL-10 levels were significantly increased. On day 7 of HFD, TNFα expression in microglia decreased to levels comparable to the chow group while that in astrocytes remained unchanged. On day 28 of HFD, TNFα levels were significantly increased in both microglia and astrocytes, which had increased mRNA expression of CD86 and MAO-B, respectively. For both glial cell types, results for TNFα expression assessed by RT-PCR and immunohistochemical analysis were similar.These results indicate that the role of microglia and astrocytes in hypothalamic inflammation under HFD conditions changed with time and these changes were accompanied by changes in the activation status of glial cells. Our data suggest that early after initiating HFD, hypothalamic astrocytes suppress diet-induced inflammation at least in part by secreting IL-10, whereas continued HFD feeding impairs this suppressive function such that both microglia and astrocytes promote hypothalamic inflammation.

ISOMORPHISMS UP TO BOUNDED TORSION BETWEEN RELATIVE -GROUPS AND CHOW GROUPS WITH MODULUS

AbstractThe purpose of this note is to establish isomorphisms up to bounded torsion between relative $K_{0}$-groups and Chow groups with modulus as defined by Binda and Saito.

Global representation of Segre numbers by Monge\u2013Amp\xe8re products

On a reduced analytic space X we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding quotient mathcal {B}(X) that we think of as an analogue of the Chow group and a refinement of de Rham cohomology. This group allows us to study both global and local intersection theoretic properties. We provide many mathcal {B}-analogues of classical intersection theoretic constructions: For an analytic subspace Vsubset X we define a mathcal {B}-Segre class, which is an element of mathcal {B}(X) with support in V. It satisfies a global King formula and, in particular, its multiplicities at each point coincide with the Segre numbers of V. When V is cut out by a section of a vector bundle we interpret this class as a Monge–Ampère-type product. For regular embeddings we construct a mathcal {B}-analogue of the Gysin morphism.

A pencil of Enriques surfaces with non-algebraic integral Hodge classes

We prove that there exists a pencil of Enriques surfaces defined over $\mathbb{Q}$ with non-algebraic integral Hodge classes of non-torsion type. This gives the first example of a threefold with the trivial Chow group of zero-cycles on which the integral Hodge conjecture fails. As an application, we construct a fourfold which gives the negative answer to a classical question of Murre on the universality of the Abel-Jacobi maps in codimension three.

Effects of resistant dextrin on liver fat deposition and the AMPK signaling pathway in high-fat diet-fed mice

Objective To study the effects of resistant dextrin (RD) on liver fat deposition in high-fat diet-fed (HFD) mice, and to further explore whether it can regulate the AMPK signaling pathway. Methods Thirty-six 4-week-old male C57BL/6 mice were randomly divided into three groups: normal control group (chow), high-fat diet group (HFD), and high-fat diet+ resistant dextrin group (HFD+ RD, 10 g·kg-1·d-1). After 12 weeks of intervention, the liver tissues and serum samples were collected. Serum triglyceride (TG), total cholesterol (TC), low-density lipoprotein-cholesterol (LDL-C), high-density lipoprotein-cholesterol (HDL-C), aspartate aminotransferase (AST), alanine transaminase (ALT) levels and liver TG were measured. Liver tissue HE and oil red O staining were performed to observe hepatocyte steatosis and liver fat deposition. Quantitative real-time PCR was performed to detect the relative expression of fatty acid synthesis related genes SREBP1, ACC, SCD1 in the liver tissue, and Western blot was performed to detect relative protein levels of pAMPK, SREBP1, Fasn, and ACC in the liver. Results Compared with chow group, the body weight gain, fasting blood glucose (FBG), serum TC, LDL-C, HDL-C, and ALT levels were increased in HFD group (P<0.01), and serum AST level was also increased (P<0.05). Moreover, liver oil red O staining revealed that liver fat deposition was much more obvious in HFD group than that in chow group, and liver TG was also increased in HFD group (P<0.01). The mRNA levels of SREBP1 and ACC were increased in HFD group compared with that in chow group, and the protein level of pAMPK was reduced in HFD group (P<0.05). As compared with HFD group, the body weight gain, serum TG, TC, LDL-C, HDL-C and ALT levels were significantly reduced in RD group (P<0.01), and FBG level was also reduced (P<0.05). Moreover, RD treatment alleviated liver fat deposition and TG accumulation (P<0.01). The mRNA levels of SREBP1, ACC, and SCD1 were all reduced in RD group compared with HFD group. The protein level of pAMPK was increased, and the expression of Fasn was reduced with RD treatment (P<0.01). Conclusion Resistant dextrin improves liver fat deposition and activates the AMPK signaling pathway in HFD-fed mice. Key words: Resistant dextrin; Fatty liver; Liver fat deposition; Adenosine monophosphate-activated protein kinase