Vol. 12, No. 8, 2018

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Tensor triangular geometry of filtered modules

Martin Gallauer

Vol. 12 (2018), No. 8, 1975–2003
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