Back to Commutative Algebra Seminar: Fall 2023
Commutative Algebra Seminar
Date: Friday, Nov 17, 2023
Time: 2:00PM - 3:00PM
Location: LCB 323
Justin Lyle
University of Arkansas
Title |
Counterexamples for Several Open Problems on the Vanishing of Ext and Tor |
Abstract |
Let R be a commutative Noetherian local ring. We discuss several properties R may satisfy that behave well under certain operations, and provide a general construction for producing local rings with some nice local behavior that satisfy one such property but not another. Through our methods we provide counterexamples for several open problems, for instance an open question of Araya on the vanishing of Ext^i(M,R), work of Yoshino on independence of totally reflexive conditions, and a famous open question on the depth of tensor products of Tor-independent modules. This talk is based on joint work with Kaito Kimura, Yuya Otake, and Ryo Takahashi. |
Commutative Algebra