Chow Group Research Articles

On complete intersections in varieties with finite-dimensional motive

Let X be a complete intersection inside a variety M with finite-dimensional motive and for which the Lefschetz-type conjecture B (M) holds. We show how conditions on the niveau filtration on the homology of X influence directly the niveau on the level of Chow groups. This leads to a generalization of Voisin's result. The latter states that if M has trivial Chow groups and if X has non-trivial variable cohomology parametrized by c-dimensional algebraic cycles, then the cycle class maps A(k)(X) -> H-2k (X) are injective for k < c. We give variants involving group actions, which lead to several new examples with finite-dimensional Chow motives.

Semistable Chow–Hall algebras of quivers and quantized Donaldson–Thomas invariants

The semi-stable ChowHa of a quiver with stability is defined as an analog of the Cohomological Hall algebra of Kontsevich and Soibelman via convolution in equivariant Chow groups of semi-stable loci in representation varieties of quivers. We prove several structural results on the semi-stable ChowHa, namely isomorphism of the cycle map, a tensor product decomposition, and a tautological presentation. For symmetric quivers, this leads to an identification of their quantized Donaldson-Thomas invariants with the Chow-Betti numbers of moduli spaces.

Chronic moderate alcohol consumption relieves high-fat high-cholesterol diet-induced liver fibrosis in a rat model.

Nonalcoholic fatty liver disease is a worldwide health issue and chronic alcohol consumption may have different effects on this disease. This study explored the role of chronic moderate alcohol consumption on high-fat high-cholesterol (HFHC) diet-induced liver fibrosis in a rodent model. Male Sprague-Dawley rats were divided into five groups: standard chow group, standard chow plus Er Guo Tou (EGT, a Chinese spirit made from fermented cereals) group, HFHC group, HFHC plus EGT group, and HFHC plus pure ethanol (EtOH) group. Rats were fed standard chow or HFHC chow for 12weeks. EGT or pure ethanol was administrated at a daily dose of 4g/kg body weight via intra-gastric gavage from week 4. At the end of week 12, hematoxylin and eosin staining, Sirius red and immunohistochemistry of liver sections were examined. The hepatic expression of F4/80, TNF-α, IL-1β, IL-6, CXCL1, CXCL2, α-SMA, Collagen, TGF-β, MMP2, MMP9, and TIMP1 was calculated. Both moderate EGT and pure ethanol did not increase plasma endotoxin in the portal vein comparing with the FHFC group. EGT and pure ethanol did not improve hepatic inflammation, but ameliorated liver fibrosis in histology. Moderate EGT and pure ethanol ameliorated HFHC diet-induced activation of Kupffer cells and hepatic stellate cells. In conclusion, chronic moderate EGT and pure ethanol could ameliorate HFHC diet-induced liver fibrosis.

Somatotropic Axis Dysfunction in Non-Alcoholic Fatty Liver Disease: Beneficial Hepatic and Systemic Effects of Hormone Supplementation

Background: Somatotropic axis dysfunction associated with non-alcoholic fatty liver disease (NAFLD) has potential multisystemic detrimental effects. Here, we analysed the effects of growth hormone (GH) and insulin-like growth factor-1 (IGF-1) supplementation on liver histology, adipokine profile and muscle function in an NAFLD model. Methods: C57BL/6 mice were fed with a high fat diet (HFD) for 12 weeks and were separated into three groups treated for 4 weeks with: (1) High fat diet (HFD) (n = 10); (2) HFD + GH 9 μg/g/d (n = 10); (3) HFD + IGF-1 0.02 µg/g/d (n = 9). A control group fed a chow diet was included (n = 6). Liver histology, liver triglycerides content, serum alanine aminotransferase (ALT) activity, adiponectin and leptin serum levels, in vivo muscle strength, tetanic force and muscle fibre cross-sectional area (CSA) were measured. Results: HFD + GH and HFD + IGF-1 groups showed significantly lower ALT activity compared to HFD (p < 0.01). Liver triglyceride content in HFD + GH was decreased compared to HFD (p < 0.01). Histologic steatosis score was increased in HFD and HFD + GH group (p < 0.01), whereas HFD + IGF-1 presented no difference compared to the chow group (p = 0.3). HFD + GH group presented lower serum leptin and adiponectin levels compared to HFD. GH and IGF-1 supplementation therapy reverted HFD-induced reduction in muscle strength and CSA (sarcopenia). Conclusions: GH and IGF-1 supplementation induced significant improvement in liver steatosis, aminotransferases and sarcopenia in a diet-induced NAFLD model.

Cohomological orientifold Donaldson–Thomas invariants as Chow groups

We establish a geometric interpretation of orientifold Donaldson–Thomas invariants of $$\sigma $$ -symmetric quivers with involution. More precisely, we prove that the cohomological orientifold Donaldson–Thomas invariant is isomorphic to the rational Chow group of the moduli space of $$\sigma $$ -stable self-dual quiver representations. As an application we prove that the Chow Betti numbers of moduli spaces of stable m-tuples in classical Lie algebras can be computed numerically. We also prove a cohomological wall-crossing formula relating semistable Hall modules for different stabilities.

Food withdrawal alters the gut microbiota and metabolome in mice.

Food withdrawal as a health-enhancing measure has beneficial effects on aging, disease prevention, and treatment. However, the cellular and molecular mechanisms involving gut microbial changes and metabolic consequences resulting from food withdrawal have yet to be elucidated. In this study, we subjected lean and obese mice to a dietary intervention that consisted of a 4-d complete food withdrawal and an 8-d 50% food withdrawal, and we studied changes in cecal microbiome and host serum metabolome. The abundance of potentially pathogenic Proteobacteria was decreased and Akkermansia muciniphila was elevated by food withdrawal in mice fed a high-fat diet (HFD). Meanwhile, food withdrawal decreased the abundance of metabolites in branched chain amino acid, lipid, and free fatty acid metabolisms in host serum, more so in HFD mice than in normal mice. Microbial predicted function also showed that food withdrawal decreased the abundance of microbes associated with predicted diseases in the HFD group but not in the normal chow group. Correlation between the microbiome data and metabolomics data revealed a strong association between gut microbial and host metabolic changes in response to food withdrawal. In summary, our results showed that food withdrawal was safer and more metabolically beneficial to HFD-induced obese mice than to normal lean mice, and the beneficial effects were primarily derived from the changes in gut microbiota, which were closely associated with the host metabolome.-Zheng, X., Zhou, K., Zhang, Y., Han, X., Zhao, A., Liu, J., Qu, C., Ge, K., Huang, F., Hernandez, B., Yu, H., Panee, J., Chen, T., Jia, W., Jia, W. Food withdrawal alters the gut microbiota and metabolome in mice.

Stable rationality of quadric and cubic surface bundle fourfolds

We study the stable rationality problem for quadric and cubic surface bundles over surfaces from the point of view of the degeneration method for the Chow group of 0-cycles. Our main result is that a very general hypersurface X of bidegree (2,3) in P^2 x P^3 is not stably rational. Via projections onto the two factors, X is a cubic surface bundle over P^2 and a conic bundle over P^3, and we analyze the stable rationality problem from both these points of view. This provides another example of a smooth family of rationally connected fourfolds with rational and nonrational fibers. Finally, we introduce new quadric surface bundle fourfolds over P^2 with discriminant curve of any even degree at least 8, having nontrivial unramified Brauer group and admitting a universally CH_0-trivial resolution.

Algebraic cycles on certain hyperkähler fourfolds with an order 3 non-symplectic automorphism II

ABSTRACTLet X be a hyperkähler variety, and assume X has a non-symplectic automorphism σ of order . Bloch’s conjecture predicts that the quotient X∕<σ> should have trivial Chow group of 0-cycles. We verify this for Fano varieties of lines on certain cubic fourfolds having an order 3 non-symplectic automorphism.

High-fat/high-sucrose diet-induced obesity results in joint-specific development of osteoarthritis-like degeneration in a rat model.

ObjectivesMetabolic syndrome and low-grade systemic inflammation are associated with knee osteoarthritis (OA), but the relationships between these factors and OA in other synovial joints are unclear. The aim of this study was to determine if a high-fat/high-sucrose (HFS) diet results in OA-like joint damage in the shoulders, knees, and hips of rats after induction of obesity, and to identify potential joint-specific risks for OA-like changes.MethodsA total of 16 male Sprague-Dawley rats were allocated to either the diet-induced obesity group (DIO, 40% fat, 45% sucrose, n = 9) or a chow control diet (n = 7) for 12 weeks. At sacrifice, histological assessments of the shoulder, hip, and knee joints were performed. Serum inflammatory mediators and body composition were also evaluated. The total Mankin score for each animal was assessed by adding together the individual Modified Mankin scores across all three joints. Linear regression modelling was conducted to evaluate predictive relationships between serum mediators and total joint damage.ResultsThe HFS diet, in the absence of trauma, resulted in increased joint damage in the shoulder and knee joints of rats. Hip joint damage, however, was not significantly affected by DIO, consistent with findings in human studies. The total Mankin score was increased in DIO animals compared with the chow group, and was associated with percentage of body fat. Positive significant predictive relationships for total Mankin score were found between body fat and two serum mediators (interleukin 1 alpha (IL-1α) and vascular endothelial growth factor (VEGF)).ConclusionSystemic inflammatory alterations from DIO in this model system may result in a higher risk for development of knee, shoulder, and multi-joint damage with a HFS diet.Cite this article: K. H. Collins, D. A. Hart, R. A. Seerattan, R. A. Reimer, W. Herzog. High-fat/high-sucrose diet-induced obesity results in joint-specific development of osteoarthritis-like degeneration in a rat model. Bone Joint Res 2018;7:274–281. DOI: 10.1302/2046-3758.74.BJR-2017-0201.R2

A novel small‐molecule inhibitor of the WNT/β‐catenin pathway show efficacy in treating diet induced alteration of glucose and lipid metabolism

WNT/β‐catenin pathway is well studied for its role in cell differentiation and proliferation. The major effector of this pathway, β‐catenin, interacts with nuclear pool of co‐transcription factors T‐cell factor/lymphoid enhancer factor (TCF/LEF) to initiate transcription of WNT downstream genes that regulate different processes including glucose and lipid metabolism. Here, we screened a library of 90 compounds using a TCF/LEF responsive reporter assay. We identified a potent quinolinium compound, YW1128, which is able to stabilize Axin levels and decrease WNT signaling (IC50 = 8 nM). In vitro validation assays and in vivo efficacy characterization for this compound using a high fat diet C57BL/6J mouse model in contrast to a normal chow mouse model of the same background were carried out. Our western blot and immunocytochemistry results confirm the WNT inhibitory effects of YW1128 in HEK293 cells. Treatment of huh7 cells led to significant decrease in lipid accumulation shown by nile red staining. In mice fed high fat diet, YW1128 alleviated fatty liver disease and slightly improved glucose tolerance as assessed by haemotoxylin and eosin staining and intraperitoneal glucose tolerance tests, respectively. With no effect on toxicity markers, YW1128 significantly decreased serum cholesterol level in high fat diet mice group with no effect in the normal chow group. Treatment mice also had significant decrease in genes involved in glucose metabolism and fatty acid metabolism pathways along with YW1128 inhibitory effect in WNT signaling pathways. To conclude, we identified an novel WNT pathway inhibitor that show promising benefit for treating diseases associated with glucose and lipid metabolism through its effect on WNT signaling pathway.Support or Funding InformationFunded by the National Institute of General Medical Sciences of the National Institutes of Health (NIH) under Award R01GM099742This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Relative K0 and relative cycle class map

Let F:A→B be an exact functor between small exact categories. We study the zeroth homotopy group K0(F) of the homotopy fiber of the map K(A)→K(B) between K-theory spectra. Under the assumption that F is a cofinal and that B is split exact, we give an explicit description of K0(F) in terms of the triangulated functor Db(A)→Db(B) between the derived categories.We apply it to the pair (X,D) of a scheme X and an affine closed subscheme D of X, and get a description of the relative K0-group K0(X,D) in terms of perfect complexes; it is generated by pairs of two perfect complexes of X together with quasi-isomorphisms along D. This description makes it possible to assign a cycle class in K0(X,D) to a cycle on X not meeting D in an intuitive way. When X is a separated regular scheme of finite type over a field and D is an affine effective Cartier divisor on X, we prove that the cycle classes induce a surjective group homomorphism from the Chow group with modulus CH⁎(X|D) defined by Binda–Saito to a suitable subquotient of K0(X,D).

An explicit basis for the rational higher Chow groups of abelian number fields

We review and simplify A. Beilinson's construction of a basis for the motivic cohomology of a point over a cyclotomic field, then promote the basis elements to higher Chow cycles and evaluate the KLM regulator map on them.

On the closed embedding of the product of theta divisors into product of Jacobians and Chow groups

In this paper, we generalize the injectivity of the push-forward homomorphism at the level of Chow groups, induced by the closed embedding of [Formula: see text] into [Formula: see text] for [Formula: see text], where [Formula: see text] is a smooth projective curve, to symmetric powers of a smooth projective variety of higher dimension. We also prove the analog of this theorem for product of symmetric powers of smooth projective varieties. As an application we prove the injectivity of the push-forward homomorphism at the level of Chow groups, induced by the closed embedding of self-product of theta divisor into the self-product of the Jacobian of a smooth projective curve.

A regulator map for 1-cycles with modulus

Let $k$ be a field of characteristic 0. We define a map from the additive higher Chow group of 1-cycles with strong sup $m$-modulus $CH_1(A_k(m), n)_{ssup}$ to the module of absolute Kähler differentials of $k$ with twisted $k^*$-action $\Omega^{n-2}_k\langle \omega \rangle$ of weight $\omega$. We will call the map a regulator map, and we show that the regulator map is surjective if $k$ is an algebraically closed field. In case $\omega = m+1$, this map specializes to Park's regulator map. We study a relationship between the cyclic homology and the additive higher Chow group with strong sup modulus by using our regulator map.

On the semi-stable CoHa and its modules arising from smooth models

We study a variant of the semi-stable Cohomological Hall algebra which we construct using equivariant Chow groups. This algebra, we call it the semi-stable ChowHa, arises as a quotient of the CoHa. Smooth models of quiver moduli give rise to modules over the semi-stable ChowHa. We prove that these modules are cyclic and we compute a presentation using Harder–Narasimhan methods.

Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians

We provide several ingredients towards a generalization of the Littlewood-Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product-formula for multiplying classes of smooth Schubert varieties with any Bott-Samelson class in algebraic cobordism of the grassmannian. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.

Algebraic cycles and EPW cubes

AbstractLet X be a hyperkähler variety with an anti‐symplectic involution ι. According to Beauville's conjectural “splitting property”, the Chow groups of X should split in a finite number of pieces such that the Chow ring has a bigrading. The Bloch–Beilinson conjectures predict how ι should act on certain of these pieces of the Chow groups. We verify part of this conjecture for a 19‐dimensional family of hyperkähler sixfolds that are “double EPW cubes” (in the sense of Iliev–Kapustka–Kapustka–Ranestad). This has interesting consequences for the Chow ring of the quotient , which is an “EPW cube” (in the sense of Iliev–Kapustka–Kapustka–Ranestad).

Electroacupuncture Reduces Weight in Diet-Induced Obese Rats via Hypothalamic Tsc1 Promoter Demethylation and Inhibition of the Activity of mTORC1 Signaling Pathway.

Subject The study aimed to investigate the mechanism of electroacupuncture reducing weight via tuberous sclerosis complex 1 (Tsc1) promoter methylation, inhibiting the mammalian target of rapamycin complex 1 (mTORC1) pathway. Materials and Methods Male Sprague-Dawley rats were divided into chow-fed group (chow group) or high-fat diet group (HF group) for 14 weeks. The obesity rats in HF group were randomly divided into electroacupuncture group (EA group) and diet-induced obesity (DIO) group, which received EA stimulation on bilateral ST25, RN12, SP6, and ST36 for 4 weeks or no further treatment, respectively. Methylation of the Tsc1 gene promoter and expression of agouti-related protein (AgRP), neuropeptide Y (NPY), and proopiomelanocortin (PoMC) were detected at the 18th week. Results At week 18, weight, body fat, and the body fat rate in DIO group were significantly higher than those of the chow and EA group. Compared with the chow group, the DIO group had increased methylation of the Tsc1 gene promoter and expression of mTORC1, AgRP, and NPY gene and decreased PoMC in the hypothalamus; after EA, methylation of the Tsc1 gene promoter, mRNA, and protein of the mTORC1 and expression of AgRP and NPY gene decreased and PoMC increased significantly. Conclusions Our study could shed light on the potential pathway where EA exerts effects on the mechanism of EA treatment for obesity through the hypothalamic Tsc1 promoter demethylation and inhibition of the activity of mTORC1 signaling pathway.

Obesity Induced by High Fat Diet Impairs Glucose Tolerance and Insulin Sensitivity in Rats

Introduction: Obesity is a chronic disease, besides a risk factor for cardiovascular diseases, nowadays, it is characterized as a worldwide epidemic. The food imbalance and physical inactivity are factors that contribute to the emergence of obesity as well as diabetes. Objective: To evaluate the injury on glucose tolerance and insulin sensitivity in obese rats induced by high fat diet. Methodology: Male Rats Wistar (8 weeks old) were submitted to the standard diet (chow group, 11.8% kcal-Lipids; n = 5) and dietary intervention with high fat diet during 8 weeks (HFD group, 58.4% kcal-Lipids; n= 5). It was evaluated the body weight weekly, and fasting and fed blood glucose. At the end of the experimental period, was measured the glucose tolerance, insulin sensitivity and gluconeogenesis. After the animal sacrifice, it was analyzed relative weight of white adipose tissue, as well as the adipocytes diameter (epididymal white adipose tissue) and circulating levels of leptin. Results and Discussion: The group HFD presented higher body weight (from the 2nd week of diet), an increase accumulation of epididymal and perirenal white adipose tissue. In addition, in these animals, it was observed a significant increase in the adipocytes diameter and the levels of leptin in plasma when compared to animals chow, indicating obesity with increased release of cytokines. In HFD group, the fasting blood glucose levels were significantly higher in the 6th week of high fat diet consumption compared to the chow group. Adding up to the frame of obesity, at the end of the 8th week of high fat diet consumption, the obese group had higher fasting plasma glucose in fed state, glucose intolerance, insulin resistance, as well as increased gluconeogenesis as compared with the chow group. Conclusion: Obesity with adipocyte hypertrophy, induced by high fat diet, induces glycemic damages, as the elevation of blood glucose, glucose intolerance and lower insulin sensitivity in rats.

A Cycle Class Map from Chow Groups with Modulus to Relative $K$-Theory

Let \overline{X} be a smooth quasi-projective d -dimensional variety over a field k and let D be an effective, non-reduced, Cartier divisor on it such that its support is strict normal crossing. In this note, we construct cycle class maps from (a variant of) the higher Chow group with modulus of the pair (\overline{X};D) in the range (d+n, n) to the relative K -groups K_n(\overline{X}; D) for every n\geq 0 .