Algebra & Number Theory

Adams operations on matrix factorizations

Michael Brown, Claudia Miller, Peder Thompson, and Mark Walker

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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.

Article information

Algebra Number Theory, Volume 11, Number 9 (2017), 2165-2192.

Received: 31 December 2016
Accepted: 9 August 2017
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 13D15: Grothendieck groups, $K$-theory [See also 14C35, 18F30, 19Axx, 19D50]
Secondary: 13D02: Syzygies, resolutions, complexes 13D09: Derived categories 13D22: Homological conjectures (intersection theorems)

Adams operations matrix factorizations Hochster's theta pairing


Brown, Michael; Miller, Claudia; Thompson, Peder; Walker, Mark. Adams operations on matrix factorizations. Algebra Number Theory 11 (2017), no. 9, 2165--2192. doi:10.2140/ant.2017.11.2165.

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