Tue, May 14, 2019
Public Access Category: All |
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- Time:
- 4:30pm-5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Commutative Algebra Seminar.
Speaker: Jyoti Singh.
Affiliation: Visvesvaraya National Institute of Technology, Nagpur.
Date and Time: Tuesday 14 May, 4:30 pm - 5:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Strongly generalized Eulerian $D$-modules.
Abstract: Let K be a field of characteristic zero and A_n(K) be the nth-Weyl
algebra over K. In this talk, we discuss strongly generalised Eulerian
$A_n(K)$-modules and their properties. We prove that if M is a strongly
generalized
Eulerian $A_n(K)$-module, then so is the graded Matlis dual of M. We also
prove that
Ext functor of strongly generalized Eulerian modules is strongly generalized
Eulerian $A_n(K)$-module. As a consequence, we prove the following
conjecture:
Let M and N be non-zero, left, holonomic, graded generalized Eulerian
$A_n(K)$-modules. Then the graded K-vector space $Ext^i_{A_n(K)}(M, N)$ is
concentrated in degree zero for any i >=0.