Vol. 6, No. 1, 2012

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
$L$-series of Artin stacks over finite fields

Shenghao Sun

Vol. 6 (2012), No. 1, 47–122
Abstract

We develop the notion of stratifiability in the context of derived categories and the six operations for stacks. Then we reprove the Lefschetz trace formula for stacks, and give the meromorphic continuation of L-series (in particular, zeta functions) of Fq-stacks. We also give an upper bound for the weights of the cohomology groups of stacks, and an “independence of ” result for a certain class of quotient stacks.

Keywords
$l$-adic cohomology, algebraic stack, Lefschetz trace formula, $L$-function
Mathematical Subject Classification 2010
Primary: 14F20
Secondary: 14F05, 19F27
Milestones
Received: 8 July 2010
Revised: 28 March 2011
Accepted: 24 April 2011
Published: 15 June 2012
Authors
Shenghao Sun
Département de Mathématiques
Bâtiment 425
Faculté des Sciences d’Orsay
Université Paris-Sud 11
F-91405 Orsay Cedex
France
http://www.math.u-psud.fr/~ssun/