A thick subcategory theorem for modules over certain ring spectra

Mathew, Akhil

doi:10.2140/gt.2015.19.2359

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A thick subcategory theorem for modules over certain ring spectra

Akhil Mathew

Geometry & Topology 19 (2015) 2359–2392

DOI: 10.2140/gt.2015.19.2359

Abstract

We classify thick subcategories of the $\infty$ –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

Volume 19, issue 4 (2015)