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Big Cohen-Macaulay modules, morphisms of perfect complexes, and intersection theorems

Hot Topics: The Homological Conjectures March 12, 2018 - March 16, 2018

March 16, 2018 (11:30 AM PDT - 12:30 PM PDT)
Speaker(s): Luchezar Avramov (University of Nebraska)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

16-Avromov

Abstract

The talk concerns morphisms between perfect complexes over commutative noetherian rings.  The central result is a criterion for the tensor-nilpotence of such morphisms, in terms of numerical invariants of complexes known as levels. The proof uses the existence of big Cohen-Macaulay modules. Applications to local rings include a strengthening of the Improved New Intersection Theorem, and short direct proofs of several results equivalent to it.  The results come from recent joint work with Iyengar and Neeman; see https://arxiv.org/abs/1711.04052

Supplements
31010?type=thumb Avramov 441 KB application/pdf Download
Video/Audio Files

16-Avromov

H.264 Video 16-Avramov.mp4 474 MB video/mp4 rtsp://videos.msri.org/data/000/030/932/original/16-Avramov.mp4 Download
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