Tue, May 14, 2019
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4:00pm [4:30pm] Jyoti Singh, Visvesvaraya National Institute of Technology, Nagpur
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.

5:00pm
6:00pm