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Constructing derived moduli stacks

Jonathan P Pridham
Geometry & Topology 17 (2013) 1417–1495
DOI: 10.2140/gt.2013.17.1417
Abstract

We introduce frameworks for constructing global derived moduli stacks associated to a broad range of problems, bridging the gap between the concrete and abstract conceptions of derived moduli. Our three approaches are via differential graded Lie algebras, via cosimplicial groups, and via quasicomonoids, each more general than the last. Explicit examples of derived moduli problems addressed here are finite schemes, polarised projective schemes, torsors, coherent sheaves and finite group schemes.

Keywords
derived algebraic geometry, stacks, derived moduli, DGLAs
Mathematical Subject Classification 2010
Primary: 14A20
Secondary: 14D23, 14J10
References
Publication
Received: 2 February 2012
Revised: 1 November 2012
Accepted: 9 February 2013
Published: 6 June 2013
Proposed: Lothar Göttsche
Seconded: Richard Thomas, Haynes Miller
Authors
Jonathan P Pridham
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Wilberforce Road
Cambridge CB3 0WB
UK
http://www.dpmms.cam.ac.uk/~jpp24