Vol. 11, No. 9, 2017

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Adams operations on matrix factorizations

Michael K. Brown, Claudia Miller, Peder Thompson and Mark E. Walker

Vol. 11 (2017), No. 9, 2165–2192
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.

Keywords
Adams operations, matrix factorizations, Hochster's theta pairing
Mathematical Subject Classification 2010
Primary: 13D15
Secondary: 13D02, 13D09, 13D22
Milestones
Received: 31 December 2016
Accepted: 9 August 2017
Published: 2 December 2017
Authors
Michael K. Brown
Department of Mathematics
University of Wisconsin-Madison
Madison, WI
United States
Claudia Miller
Mathematics Department
Syracuse University
Syracuse, NY
United States
Peder Thompson
Department of Mathematics and Statistics
Texas Tech University
Lubbock, TX
United States
Mark E. Walker
Deptartment of Mathematics
University of Nebraska-Lincoln
Lincoln, NE
United States