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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



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

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