共查询到20条相似文献,搜索用时 31 毫秒
1.
Michael Jöllenbeck 《Journal of Pure and Applied Algebra》2006,207(2):261-298
In this paper we study the multigraded Hilbert and Poincaré-Betti series of A=S/a, where S is the ring of polynomials in n indeterminates divided by the monomial ideal a. There is a conjecture about the multigraded Poincaré-Betti series by Charalambous and Reeves which they proved in the case where the Taylor resolution is minimal. We introduce a conjecture about the minimal A-free resolution of the residue class field and show that this conjecture implies the conjecture of Charalambous and Reeves and, in addition, gives a formula for the Hilbert series. Using Algebraic Discrete Morse theory, we prove that the homology of the Koszul complex of A with respect to x1,…,xn is isomorphic to a graded commutative ring of polynomials over certain sets in the Taylor resolution divided by an ideal r of relations. This leads to a proof of our conjecture for some classes of algebras A. We also give an approach for the proof of our conjecture via Algebraic Discrete Morse theory in the general case.The conjecture implies that A is Golod if and only if the product (i.e. the first Massey operation) on the Koszul homology is trivial. Under the assumption of the conjecture we finally prove that a very simple purely combinatorial condition on the minimal monomial generating system of a implies Golodness for A. 相似文献
2.
V. A. Bovdi A. B. Konovalov S. Siciliano 《Rendiconti del Circolo Matematico di Palermo》1932,56(1):125-136
We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic groupM 12. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs. 相似文献
3.
We classify the radical subgroups and chains of the Conway simple group Co1 and then verify the Alperin weight conjecture and the Dade final conjecture for this group. 相似文献
4.
V. A. Bovdi 《代数通讯》2013,41(7):2670-2680
We investigate the classical Zassenhaus conjecture for the unit group of the integral group ring of Mathieu simple group M 23 using the Luthar–Passi method. This work is a continuation of the research that we carried out for Mathieu groups M 11 and M 12. As a consequence, for this group we confirm Kimmerle's conjecture on prime graphs. 相似文献
5.
Let R be a real closed field. The Pierce–Birkhoff conjecture says that any piecewise polynomial function f on R
n
can be obtained from the polynomial ring R[x
1,..., x
n
] by iterating the operations of maximum and minimum. The purpose of this paper is threefold. First, we state a new conjecture,
called the Connectedness conjecture, which asserts, for every pair of points , the existence of connected sets in the real spectrum of R[x
1,..., x
n
], satisfying certain conditions. We prove that the Connectedness conjecture implies the Pierce–Birkhoff conjecture. Secondly,
we construct a class of connected sets in the real spectrum which, though not in itself enough for the proof of the Pierce–Birkhoff
conjecture, is the first and simplest example of the sort of connected sets we really need, and which constitutes the first
step in our program for a proof of the Pierce–Birkhoff conjecture in dimension greater than 2. Thirdly, we apply these ideas
to give two proofs that the Connectedness conjecture (and hence also the Pierce–Birkhoff conjecture in the abstract formulation)
holds locally at any pair of points , one of which is monomial. One of the proofs is elementary while the other consists in deducing this result as an immediate
corollary of the main connectedness theorem of this paper. 相似文献
6.
Chính T. Hong 《Journal of Graph Theory》1995,19(2):271-279
We investigate the conjecture that a graph is perfect if it admits a two-edge-coloring such that two edges receive different colors if they are the nonincident edges of a P4 (chordless path with four vertices). Partial results on this conjecture are given in this paper. © 1995 John Wiley & Sons, Inc. 相似文献
7.
Andrei Negut 《Inventiones Mathematicae》2009,178(2):299-331
This paper contains a proof of a conjecture of Braverman concerning Laumon quasiflag spaces. We consider the generating function
Z(m), whose coefficients are the integrals of the equivariant Chern polynomial (with variable m) of the tangent bundles of the Laumon spaces. We prove Braverman’s conjecture, which states that Z(m) coincides with the eigenfunction of the Calogero-Sutherland hamiltonian, up to a simple factor which we specify. This conjecture
was inspired by the work of Nekrasov in the affine
[^( \mathfrak sl)]n\widehat{ {\mathfrak {sl}}}_{n}
setting, where a similar conjecture is still open. 相似文献
8.
In modern number theory there are famous theorems on the modularity of Dirichlet series attached to geometric or arithmetic
objects. There is Hecke’s converse theorem, Wiles proof of the Taniyama-Shimura conjecture, and Fermat’s Last Theorem to name
a few. In this article in the spirit of the Langlands philosophy we raise the question on the modularity of the GL2-twisted spinor L-function Z
G
⊗
h
(s) related to automorphic forms G,h on the symplectic group GSp2 and GL2. This leads to several promising results and finally culminates into a precise very general conjecture. This gives new insights
into the Miyawaki conjecture on spinor L-functions of modular forms. We indicate how this topic is related to Ramakrishnan’s
work on the modularity of the Rankin-Selberg L-series. 相似文献
9.
V. A. Belonogov 《Proceedings of the Steklov Institute of Mathematics》2013,283(1):6-23
Previously, the author made the following conjecture: if a finite group has two semiproportional irreducible characters φ and ψ, then φ(1) = ψ(1). In the present paper, a new confirmation of the conjecture is obtained. Namely, the conjecture is verified for symplectic groups Sp4(q) and PSp4(q). 相似文献
10.
The paper is concerned with a problem in the theory of congruence function fields which is analogous to a conjecture of Gross in Iwasawa Theory. Zp-extensions K∞/K0 of congruence function fields K0 of characteristic p≠2 involving no new constants are considered such that the set S of ramified primes is finite and these primes are fully ramified. Is the set of S-classes invariant under Gal(K∞/K0) finite ? Gross' conjecture asserts that a similar question has an affirmative answer for the class of cyclotomic Zp- extensions of CM-type if S is the set of p-primes and the classes considered are minus S-classes. Using a formula of Witt for the norm residue symbol in cyclic p-extensions of local fields of characteristic p, a necessary and sufficient condition for the validity of the analogue of Gross' conjecture is given for a class of extensions K∞/K0. It is shown by examples that the analogue of Gross' conjecture is not always true. 相似文献
11.
Mohamed H. El-Zahar 《Journal of Graph Theory》1997,26(3):155-163
An induced subgraph S of a graph G is called a derived subgraph of G if S contains no isolated vertices. An edge e of G is said to be residual if e occurs in more than half of the derived subgraphs of G. We introduce the conjecture: Every non-empty graph contains a non-residual edge. This conjecture is implied by, but weaker than, the union-closed sets conjecture. We prove that a graph G of order n satisfies this conjecture whenever G satisfies any one of the conditions: δ(G) ≤ 2, log2 n ≤ δ(G), n ≤ 10, or the girth of G is at least 6. Finally, we show that the union-closed sets conjecture, in its full generality, is equivalent to a similar conjecture about hypergraphs. © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 155–163, 1997 相似文献
12.
Kento Fujita 《Central European Journal of Mathematics》2014,12(1):14-27
For a log Fano manifold (X,D) with D ≠ 0 and of the log Fano pseudoindex ≥2, we prove that the restriction homomorphism Pic(X) → Pic(D 1) of Picard groups is injective for any irreducible component D 1 ? D. The strategy of our proof is to run a certain minimal model program and is similar to Casagrande’s argument. As a corollary, we prove that the Mukai conjecture (resp. the generalized Mukai conjecture) implies the log Mukai conjecture (resp. the log generalized Mukai conjecture). 相似文献
13.
V. A. Bovdi A. B. Konovalov S. Siciliano 《Rendiconti del Circolo Matematico di Palermo》2007,56(1):125-136
We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic groupM
12. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs.
The research was supported by OTKA grants No. T 43034, No.K61007 and Francqui Stichting (Belgium) grant ADSI107. 相似文献
14.
Amalendu Krishna 《K-Theory》2005,35(1-2):139-158
We study K2 of one-dimensional local domains which are essentially of finite type over a field of characteristic 0. In particular, we
show that Berger’s conjecture implies Geller’s conjecture for such rings. This verifies Geller’s conjecture in many new cases
of interest.
Received: September 2003 相似文献
15.
The conjecture of H.J. Zassenhaus for finite subgroups of units of integral group rings. restricted to p-subgroups, is proved for finite Frobenius groups when p is an odd prime. The result for 2-subgroups is established for those Frobenius groups that cannot be mapped homo-morphically onto S$sub:5$esub:. The conjecture in its full strength is proved for A5, S5 and SL(2.5). 相似文献
16.
Yannan Qiu 《Israel Journal of Mathematics》2012,191(1):227-278
We conjecture that local theta correspondence can be normalized by the leading coefficient of a weighted local period integral, and that there exists a duality of local and global inner product formulas. The conjecture is verified for the pair (, PGL 2) and (SL 2, SO(2, 2)). As an application, global inner product formulas are obtained for liftings in the directions PGL 2 → , GSO(2, 2) → GL 2. 相似文献
17.
James M. Turner 《Journal of Pure and Applied Algebra》2009,213(7):1224-1238
In [D. Quillen, On the (co)homology of commutative rings, Proc. Symp. Pure Math. 17 (1970) 65-87; L. Avramov, Locally complete intersection homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology, Annals of Math. 2 (150) (1999) 455-487] a conjecture was posed to the effect that if R→A is a homomorphism of Noetherian commutative rings then the flat dimension, as defined in the derived category of A-modules, of the associated cotangent complex LA/R satisfies: . The aim of this paper is to initiate an approach for solving this conjecture when R has characteristic 2 using simplicial algebra techniques. To that end, we obtain two results. First, we prove that the conjecture can be reframed in terms of certain nilpotence properties for the divided square γ2 and the André operation ? as it acts on TorR(A,?), ? any residue field of A. Second, we prove the conjecture is valid in two cases: when and when R is a Cohen-Macaulay ring. 相似文献
18.
19.
We prove, over a p-adic local field F, that an irreducible supercuspidal representation of GL2n
(F) is a local Langlands functorial transfer from SO2n+1(F) if and only if it has a nonzero Shalika model (Corollary 5.2, Proposition 5.4 and Theorem 5.5). Based on this, we verify
(Sect. 6) in our cases a conjecture of Jacquet and Martin, a conjecture of Kim, and a conjecture of Speh in the theory of
automorphic forms. 相似文献
20.
Let G be a simply connected semisimple complex Lie group and fix a maximal
unipotent subgroup U- of G. Let q be an indeterminate and let B* denote the dual canonical basis (cf. [19]) of the quantized algebra Cq[U-] of regular functions on U-. Following [20], fix a ZN≧0-parametrization of this basis, where N = dim U-. In [2], A. Berenstein and A. Zelevinsky conjecture that two elements of B* q-commute if and only if they are multiplicative,
i.e., their product is an element of B* up to a power of q. To any reduced decomposition w0 of the longest element of the Weyl group of g, we associate a subalgebra Aw0, called adapted algebra, of Cq[U-] such that (1) Aw0 is a q-polynomial algebra which equals Cq[U-] up to localization, (2) Aw0 is spanned by a subset of B*, (3) the Berenstein–Zelevinsky conjecture is true on Aw0. Then we test the conjecture when one element belongs to the q-center of Cq[U-]. 相似文献