Tensor triangular geometry of filtered modules

Gallauer Alves de Souza, Martin

doi:10.2140/ant.2018.12.1975

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Tensor triangular geometry of filtered modules

Martin Gallauer

Vol. 12 (2018), No. 8, 1975–2003

DOI: 10.2140/ant.2018.12.1975

Abstract

We compute the tensor triangular spectrum of perfect complexes of filtered modules over a commutative ring and deduce a classification of the thick tensor ideals. We give two proofs: one by reducing to perfect complexes of graded modules which have already been studied in the literature by Dell’Ambrogio and Stevenson (2013, 2014) and one more direct for which we develop some useful tools.

Keywords

tensor triangular geometry, filtered modules, classification

Mathematical Subject Classification 2010

Primary: 18E30

Secondary: 18D10, 55U35

Milestones

Received: 29 October 2017

Revised: 13 March 2018

Accepted: 12 June 2018

Published: 4 December 2018

Authors

Martin Gallauer
Department of Mathematics University of California, Los Angeles Los Angeles, CA United States

Vol. 12, No. 8, 2018