Adams Operations on Matrix Factorizations
Michael K. Brown, Claudia Miller, Peder Thompson, Mark E. Walker
TL;DR
This paper introduces Adams operations on matrix factorizations, demonstrating their key properties and applying them to prove a conjecture related to Hochster's theta invariant.
Contribution
It develops Adams operations for matrix factorizations and applies them to resolve a conjecture in algebraic geometry.
Findings
Adams operations on matrix factorizations mimic properties of those on perfect complexes.
Proves a conjecture of Dao-Kurano on the vanishing of Hochster's theta invariant.
Establishes a new framework connecting Adams operations with matrix factorizations.
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-Soul\'e in their paper "Intersection Theory Using Adams Operations". As an application, we give a proof of a conjecture of Dao-Kurano concerning the vanishing of Hochster's theta invariant.
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