Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
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Counterexamples for Several Open Problems on the Vanishing of Ext and Tor
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.
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