Prime Degree Research Articles

Indices of Kummer extensions of prime degree

Let p be a prime and let ζp be a primitive p-th root of unity. For a finite extension k of Q containing ζp, we consider a Kummer extension L/k of degree p. In this paper, we show that if k=Q(ζp) and the class number of k is one, the index of L/k is one. We also show that if L/k is tamely ramified with a normal integral basis, the index is at most a power of p. In the last section, we show that there exist infinitely many cubic Kummer extensions of Q(ζ3) for both wildly and tamely ramified cases, whose integer rings do not have a power integral basis over that of Q(ζ3).

Individual differences in orthographic priming relate to phonological decoding skill in adults.

We examined relationships between individual differences in orthographic priming and a battery of measures assessing orthographic processing ability, reading history, current reading ability, and verbal intelligence in university students. Pronounceable and unpronounceable nonword primes preceded word and nonword targets. Individual differences in nonword reading skill and other measures of reading and spelling ability were associated with the degree of orthographic priming. Individuals with less phonological decoding skill benefited more from anagram primes for word targets preceded by unpronounceable primes and nonword targets preceded by pronounceable primes. Analyses of extreme groups revealed that the group with the lowest phonemic decoding efficiency scores showed a general benefit of orthographic relatedness, while the group with the highest phonemic decoding efficiency scores showed a benefit only under certain conditions. Thus, individuals with worse nonword reading skills may have less precise orthographic representations and therefore benefit more from overlapping coarse-grained orthographic information, regardless of the pronounceability of the prime or the lexical status of the target. These findings demonstrate that university students vary in their orthographic processing skill and the degree to which orthographic information is used during word recognition.

Limitation of Improvement in Germination by Osmopriming of Differentially Aged Non-Orthodox Neem (Azadirachta indica) Seeds

This work involves physiological and biochemical features of seed ageing gauged from seed viability and vigour over the period of storage. Both conventional storage (natural ageing) and controlled deterioration (accelerated ageing) are resulted in loss of germination capacity and vigour as well as poor seedling establishment. Present findings indicate that both natural and accelerated ageing sustain similar pattern, except their mortality curve. In natural ageing, prior to entering sigmoidal type decline a period of relative stability exists; whereas in accelerated aging, such relative stability is absent. It is also observed that rate- controlling process of ageing (natural ageing slow whereas accelerated ageing fast) was dependent upon moisture content and temperature. These physical factors have negative linear correlation with seed viability. Membrane integrity and lipid peroxidation are associated with seed ageing, however peroxidation does not hold exact with accelerated ageing. Additionally, these aged seeds were exposed to osmopriming (controlled hydration) resulted in improved germination characterized by faster and uniform germination. For the first time, it was strongly established that osmopriming significantly improves the seed germination (about 12- 17%) until a critical level (up to 50% germination) during the ageing and thereafter priming does not support the process of improvement of germination. Such improvement prediction is important for physiologists and seed technologists to recruitment the degree of priming.

On the solvability of an Eisenstein trinomial of prime degree

Let f(X)=Xp+acp−2X+acp−1 be a trinomial of prime degree p≥7 that is Eisenstein with respect to p, where a and c are coprime rational integers. We investigate the following question, linked to a conjecture formulated by Kolle and Schmid: is it possible for f(X) to be solvable over ℚ? The main tool in this study is the determination of the decomposition group at a place above some primes that do not ramify in the splitting field of f(X).

Statins Potentiate the Cytotoxic Effect of ABT-199 in Diffuse Large B Cell Lymphoma

BCL-2 is a key pro-survival protein that is highly expressed in many leukemias and lymphomas. ABT-199 (venetoclax) is a small molecule inhibitor of BCL-2 that has demonstrated impressive responses in chronic lymphocytic leukemia (CLL) leading to FDA approval for second line treatment of patients with 17p deletion. However, other hematologic malignancies are less responsive to ABT-199 as a single agent, suggesting that combinations of targeted therapies may be required to elicit more promising responses. We have investigated the potential of combining ABT-199 with HMG-CoA reductase (HMGCR) inhibitors (statins), which have known anti-cancer potential in hematologic malignancies. Using multiple chemically distinct statin compounds, we observed profound synergistic induction of apoptosis when combined with ABT-199 in both human diffuse large B cell lymphoma (DLBCL) as well as acute myeloid leukemia (AML) cell lines. This synergy was also seen in primary murine B lymphoma cells over-expressing MYC and BCL-2. Importantly, addition of exogenous mevalonate completely rescued cells from the combination, confirming on-target efficacy of HMGCR inhibition. Using BH3 profiling, we found that simvastatin significantly primed lymphoma cells for undergoing apoptosis (termed mitochondrial priming). Notably, the degree of priming correlated with its ability to synergize with ABT-199, suggesting that BH3 profiling may be used to predict patient responses. The combination did not synergize to kill normal human peripheral blood mononuclear cells from healthy donors, suggesting that statins may selectively prime cancer cells for apoptosis. Mechanistic studies support the hypothesis that statins synergize with ABT-199 by suppressing protein prenylation, particularly protein geranylgeranylation. In support, the addition of exogenous geranylgeranyl pyrophosphate (GGPP) completely rescued cells from the effects of simvastatin. Furthermore, selective inhibition of protein geranylgeranyl transferase (GGT) increased priming and was sufficient to recapitulate the effects of simvastatin in combination with ABT-199. Statins and GGT inhibitors increased the mitochondrial abundance of a subset of BH3-only pro-apoptotic proteins. Lastly, we have identified Rap1A de-prenylation as a marker of pharmacodynamic response to statins in vivo. Thus, this project highlights a novel combination for use in aggressive lymphomas, establishes its efficacy and tolerability using preclinical models, and provides proof-of-concept to warrant investigation of its clinical potential. DisclosuresLetai:AbbVie: Consultancy, Research Funding; Astra-Zeneca: Consultancy, Research Funding; Tetralogic: Consultancy, Research Funding.

A note on the existence of cyclic algebras in division algebras

ABSTRACTLet F be a Henselian field such that is a global field. It is shown that if D is an F-central division algebra such that then D contains a cyclic division algebra of prime degree even though D can be a noncrossed product. Here, our approach is based on the Albert’s cyclicity criterion and centralizer theorem.

Characters of the norm-one units of local division algebras of prime degree

We give an explicit construction of all complex continuous irreducible characters of the group SL1(D), where D is a division algebra of prime degree ℓ over a local field of odd residual characteristic different from ℓ. For ℓ odd, we show that all such characters of SL1(D) are induced from linear characters of compact-open subgroups of SL1(D). We also compute an explicit formula for the representation zeta function of SL1(D).

Symbol p-algebras of prime degree and their p-central subspaces

We prove that the maximal dimension of a p-central subspace of the generic symbol p-algebra of prime degree p is \({p+1}\). We do it by proving the following number theoretic fact: let \({\{s_1,\dots,s_{p+1} \}}\) be \({p+1}\) distinct nonzero elements in the additive group \({G=(\mathbb{Z}/p \mathbb{Z}) \times (\mathbb{Z}/p \mathbb{Z})}\), then every nonzero element \({g \in G}\) can be expressed as \({d_1 s_1+\dots+d_{p+1} s_{p+1}}\) for some non-negative integers \({d_1,\dots,d_{p+1}}\) with \({d_1+\dots+d_{p+1} \leq p-1}\).

On prime degree isogenies between K3 surfaces

We classify prime order isogenies between algebraic K3 surfaces whose rational transcendental Hodges structures are not isometric. The morphisms of Hodge structures induced by these isogenies are correspondences by algebraic classes on the product fourfolds; however, they do not satisfy the hypothesis of the well-known Mukai--Nikulin theorem. As an application we describe isogenies obtained from K3 surfaces with an action of a symplectic automorphism of prime order.

Local base change via Tate cohomology

We propose a new way to realize cyclic base change (a special case of Langlands functoriality) for prime degree extensions of characteristic zero local fields. Let F / E F / E be a prime degree l l extension of local fields of residue characteristic p ≠ l p \neq l . Let π \pi be an irreducible cuspidal l l -adic representation of G L n ( E ) \mathrm {GL}_n(E) and let ρ \rho be an irreducible cuspidal l l -adic representation of G L n ( F ) \mathrm {GL}_n(F) which is Galois-invariant. Under some minor technical conditions on π \pi and ρ \rho (for instance, we assume that both are level zero) we prove that the mod l \bmod \,l -reductions r l ( π ) r_l(\pi ) and r l ( ρ ) r_l(\rho ) are in base change if and only if the Tate cohomology of ρ \rho with respect to the Galois action is isomorphic, as a modular representation of G L n ( E ) \mathrm {GL}_n(E) , to the Frobenius twist of r l ( π ) r_l(\pi ) . This proves a special case of a conjecture of Treumann and Venkatesh as they investigate the relationship between linkage and Langlands functoriality.

Cyclic covers that are not stably rational

Using methods developed by Kollár, Voisin, ourselves and Totaro, we prove that a cyclic cover of , , of prime degree , ramified along a very general hypersurface of degree , is not stably rational if . In dimension 3 we recover double covers of ramified along a very general surface of degree 4 (Voisin) and double covers of ramified along a very general surface of degree 6 (Beauville). We also find double covers of ramified along a very general hypersurface of degree 6. This method also enables us to produce examples over a number field.

Hoffmann’s conjecture for totally singular forms of prime degree

One of the most significant discrete invariants of a quadratic form $\phi$ over a field $k$ is its (full) splitting pattern, a finite sequence of integers which describes the possible isotropy behaviour of $\phi$ under scalar extension to arbitrary overfields of $k$. A similarly important, but more accessible variant of this notion is that of the Knebusch splitting pattern of $\phi$, which captures the isotropy behaviour of $\phi$ as one passes over a certain prescribed tower of $k$-overfields. In this paper, we determine all possible values of this latter invariant in the case where $\phi$ is totally singular. This includes an extension of Karpenko's theorem (formerly Hoffmann's conjecture) on the possible values of the first Witt index to the totally singular case. Contrary to the existing approaches to this problem (in the nonsingular case), our results are achieved by means of a new structural result on the higher anisotropic kernels of totally singular quadratic forms. Moreover, the methods used here readily generalise to give analogous results for arbitrary Fermat-type forms of degree $p$ over fields of characteristic $p>0$. Related problems concerning the Knebusch splitting of symmetric bilinear forms over fields of characteristic 2 and the full splitting of totally singular quadratic forms are also considered.

Finite groups with exactly one composite character degree

Motivated by Isaacs and Passman’s characterization of finite groups all of whose nonlinear complex irreducible characters have prime degrees, we investigate finite groups [Formula: see text] with exactly one character degree that is not a prime. We show that either [Formula: see text] is solvable with [Formula: see text] or [Formula: see text] for distinct primes [Formula: see text], or up to an abelian direct factor, [Formula: see text] is isomorphic to the alternating group [Formula: see text].

Abstract 3851: Synergy between statins and BCL-2 inhibitors in blood cancers

Abstract BCL-2 is a key pro-survival protein that is highly expressed in many leukemias and lymphomas. ABT-199 (venetoclax) is a small molecule inhibitor of BCL-2 that has demonstrated promising clinical potential in chronic lymphocytic leukemia (CLL). However, other hematologic malignancies are less responsive to ABT-199 as a single agent, suggesting that combinations of targeted therapies may be required to elicit more promising responses. We have investigated the potential of combining ABT-199 with HMG-CoA reductase (HMGCR) inhibitors (statins), which have known anti-cancer potential in hematologic malignancies. Using multiple chemically distinct statin compounds, we observed profound synergistic induction of apoptosis when combined with ABT-199 in both human diffuse large B cell lymphoma (DLBCL) as well as acute myeloid leukemia (AML) cell lines. This synergy was also seen in primary murine B lymphoma cells over-expressing MYC and BCL-2. Importantly, addition of exogenous mevalonate completely rescued cells from the combination, confirming on-target efficacy of HMGCR inhibition. Using BH3 profiling, we found that simvastatin significantly primed lymphoma cells for undergoing apoptosis (termed mitochondrial priming). Notably, the degree of priming correlated with its ability to synergize with ABT-199, suggesting that this method may be used to predict patient responses. Strikingly, the combination did not synergize to kill normal human peripheral blood mononuclear cells from healthy donors, suggesting that statins may selectively prime cancer cells for apoptosis. Mechanistic studies support the hypothesis that statins synergize with ABT-199 by suppressing protein prenylation, particularly protein geranylgeranylation. In support, the addition of exogenous geranylgeranyl pyrophosphate (GGPP) completely rescued cells from the effects of simvastatin. Furthermore, selective inhibition of protein geranylgeranyl transferase (GGT) was sufficient to recapitulate the effects of simvastatin in combination with ABT-199. Lastly, we have identified Rap1A de-prenylation as a marker of pharmacodynamic response to statins in vivo. Thus, this project highlights a novel combination for use in aggressive lymphomas, establishes its efficacy and tolerability using preclinical models, and provides proof-of-concept to warrant investigation of its clinical potential. Citation Format: Jong-Hoon S. Lee, Thanh-Trang T. Vo, David A. Fruman. Synergy between statins and BCL-2 inhibitors in blood cancers. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr 3851.

Wild immunology assessed by multidimensional mass cytometry.

A great part of our knowledge on mammalian immunology has been established in laboratory settings. The use of inbred mouse strains enabled controlled studies of immune cell and molecule functions in defined settings. These studies were usually performed in specific-pathogen free (SPF) environments providing standardized conditions. In contrast, mammalians including humans living in their natural habitat are continuously facing pathogen encounters throughout their life. The influences of environmental conditions on the signatures of the immune system and on experimental outcomes are yet not well defined. Thus, the transferability of results obtained in current experimental systems to the physiological human situation has always been a matter of debate. Studies elucidating the diversity of "wild immunology" imprintings in detail and comparing it with those of "clean" lab mice are sparse. Here, we applied multidimensional mass cytometry to dissect phenotypic and functional differences between distinct groups of laboratory and pet shop mice as a source for "wild mice". For this purpose, we developed a 31-antibody panel for murine leukocyte subsets identification and a 35-antibody panel assessing various cytokines. Established murine leukocyte populations were easily identified and diverse immune signatures indicative of numerous pathogen encounters were classified particularly in pet shop mice and to a lesser extent in quarantine and non-SPF mice as compared to SPF mice. In addition, unsupervised analysis identified distinct clusters that associated strongly with the degree of pathogenic priming, including increased frequencies of activated NK cells and antigen-experienced B- and T-cell subsets. Our study unravels the complexity of immune signatures altered under physiological pathogen challenges and highlights the importance of carefully adapting laboratory settings for immunological studies in mice, including drug and therapy testing. © 2016 International Society for Advancement of Cytometry.

An optimal representation for the trace zero subgroup

We give an optimal-size representation for the elements of the trace zero subgroup of the Picard group of an elliptic or hyperelliptic curve of any genus, with respect to a field extension of any prime degree. The representation is via the coefficients of a rational function, and it is compatible with scalar multiplication of points. We provide efficient compression and decompression algorithms, and complement them with implementation results. We discuss in detail the practically relevant cases of small genus and extension degree, and compare with the other known compression methods.

Motivic decomposition of compactifications of certain group varieties

Abstract Let D be a central simple algebra of prime degree over a field and let E be an 𝐒𝐋 1 ⁡ ( D ) {\operatorname{\mathbf{SL}}_{1}(D)} -torsor. We determine the complete motivic decomposition of certain compactifications of E. We also compute the Chow ring of E.

Kummer spaces in symbol algebras of prime degree

We classify the monomial Kummer subspaces of division symbol algebras of prime degree p, showing that every such space is standard, and in particular the dimension is no greater than p+1. It follows that in a generic symbol algebra, the dimension of any Kummer subspace is at most p+1.

On the symmetric determinantal representations of the Fermat curves of prime degree

We prove that the defining equations of the Fermat curves of prime degree cannot be written as the determinant of symmetric matrices with entries in linear forms in three variables with rational coefficients. In the proof, we use a relation between symmetric matrices with entries in linear forms and non-effective theta characteristics on smooth plane curves. We also use some results of Gross–Rohrlich on the rational torsion points on the Jacobian varieties of the Fermat curves of prime degree.

On l-class groups of global function fields

Let [Formula: see text] be a finite geometric separable extension of the rational function field [Formula: see text], and let [Formula: see text] be a finite cyclic extension of [Formula: see text] of prime degree [Formula: see text]. Assume that the ideal class number of the integral closure [Formula: see text] of [Formula: see text] in [Formula: see text] is not divisible by [Formula: see text]. Using genus theory and Conner–Hurrelbrink exact hexagon for function fields, we study in this paper the [Formula: see text]-class group of [Formula: see text] (i.e. the Sylow [Formula: see text]-subgroup of the ideal class group of [Formula: see text]) as Galois module, where [Formula: see text] is the integral closure of [Formula: see text] in [Formula: see text]. The resulting conclusion is used to discuss the relations of class numbers for the biquadratic function fields with their quadratic subfields.