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A thick subcategory theorem for modules over certain ring spectra

Akhil Mathew

Geometry & Topology 19 (2015) 2359–2392
Abstract

We classify thick subcategories of the –categories of perfect modules over ring spectra which arise as functions on even periodic derived stacks satisfying affineness and regularity conditions. For example, we show that the thick subcategories of perfect modules over TMF are in natural bijection with the subsets of the underlying space of the moduli stack of elliptic curves which are closed under specialization.

Keywords
thick subcategories, topological modular forms, derived stacks
Mathematical Subject Classification 2010
Primary: 55P43, 18E30
References
Publication
Received: 24 June 2014
Revised: 12 October 2014
Accepted: 12 November 2014
Published: 29 July 2015
Proposed: Paul Goerss
Seconded: Haynes Miller, Mark Behrens
Authors
Akhil Mathew
Department of Mathematics
University of California, Berkeley
Office 854
Berkeley, CA 94720
USA
http://math.berkeley.edu/~amathew