It is proved for certain graded non-commutative rings that if M and N are graded bi-modules, finitely generated from either side, then the Ext groups between M and N vanish from some step if and only if the Ext groups between N and M vanish from some step. Among the rings in question are twisted homogeneous coordinate rings of elliptic curves.

Given a vertex operator algebra V, one can construct two associative algebras, the Zhu A(V) and C2-algebra R(V). This gives rise to abelian categories A(V)-Mod R(V)-Mod, in addition category of admissible modules V. In case V is rational C2-cofinite, V-modules all A(V)-modules are equivalent. However, when not rational, connection between these unclear. The goal this paper study triplet W(p), a...

A cohomological support, Supp A (M), is defined for finitely generated modules M over a left noetherian ring R, with respect to a ring A of central cohomology operations on the derived category of R-modules. It is proved that if the A-module Ext R (M, M) is noetherian and Ext R (M, R) = 0 for i ≫ 0, then every closed subset of Supp A (M) is the support of some finitely generated R-module. This ...

We construct a certain topological algebra Ext♯G∨X(χ) from a Deligne-Langlands parameter space X(χ) attached to the group of rational points of a connected split reductive algebraic group G over a non-Archimedean local field K. Then we prove the equivalence between the category of continuous modules of Ext♯G∨X(χ) and the category of unramified admissible modules of G(K) with a generalized infin...

In this paper, we principally explore flat modules over a commutative ring with identity. We do this in relation to projective and injective modules with the help of derived functors like Tor and Ext. We also consider an extension of the property of flatness and induce analogies with the “special cases” occurring in flat modules. We obtain some results on flatness in the context of a noetherian...

One of the most important computations in algebraic geometry or commutative algebra that a computer algebra system should provide is the computation of finite free resolutions of ideals and modules. Resolutions are used as an aid to understand the subtle nature of modules and are also a basis of further computations, such as computing sheaf cohomology, local cohomology, Ext, Tor, etc. Modern me...

We describe the modules Dλ↓Σn−1 and D λ↑n+1 for certain simple KΣn-modules (completely splittable and some close to) D, where K is a field of characteristic p > 0 and Σn is the symmetric group of degree n. This result is based on an upper bound of the dimensions of the Ext-spaces between some simple modules.

Bounds for the Castelnuovo-Mumford regularity of Ext modules, over a polynomial ring over a field, are given in terms of the initial degrees, Castelnuovo-Mumford regularities and number of generators of the two graded modules involved. These general bounds are refined in the case the second module is the ring. Other estimates, for instance on the size of graded pieces of these modules, are give...

Let (R, m) and (S, n) be commutative Noetherian local rings, and let φ : R→ S be a flat local homomorphism such that mS = n and the induced map on residue fields R/m→ S/n is an isomorphism. Given a finitely generated R-module M , we show that M has an S-module structure compatible with the given R-module structure if and only if Ext R (S,M) = 0 for each i ≥ 1. We say that an S-module N is exten...