Adams operations on matrix factorizations

Michael Brown; Claudia Miller; Peder Thompson; Mark Walker

doi:10.2140/ant.2017.11.2165

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Home > Journals > Algebra Number Theory > Volume 11 > Issue 9 > Article

2017 Adams operations on matrix factorizations

Michael Brown, Claudia Miller, Peder Thompson, Mark Walker

Algebra Number Theory 11(9): 2165-2192 (2017). DOI: 10.2140/ant.2017.11.2165

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Abstract

We define Adams operations on matrix factorizations, and we show these operations enjoy analogues of several key properties of the Adams operations on perfect complexes with support developed by Gillet and Soulé. As an application, we give a proof of a conjecture of Dao and Kurano concerning the vanishing of Hochster’s $θ$ pairing.

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Michael Brown. Claudia Miller. Peder Thompson. Mark Walker. "Adams operations on matrix factorizations." Algebra Number Theory 11 (9) 2165 - 2192, 2017. https://doi.org/10.2140/ant.2017.11.2165

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Received: 31 December 2016; Accepted: 9 August 2017; Published: 2017

First available in Project Euclid: 20 December 2017

zbMATH: 06818948

MathSciNet: MR3735465

Digital Object Identifier: 10.2140/ant.2017.11.2165

Subjects:

Primary: 13D15

Secondary: 13D02 , 13D09 , 13D22

Keywords: Adams operations , Hochster's theta pairing , matrix factorizations

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Michael Brown, Claudia Miller, Peder Thompson, Mark Walker "Adams operations on matrix factorizations," Algebra & Number Theory, Algebra Number Theory 11(9), 2165-2192, (2017)

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