L-series of Artin stacks over finite fields

Sun, Shenghao

doi:10.2140/ant.2012.6.47

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$L$-series of Artin stacks over finite fields

Shenghao Sun

Vol. 6 (2012), No. 1, 47–122

DOI: 10.2140/ant.2012.6.47

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 $F_{q}$ -stacks. We also give an upper bound for the weights of the cohomology groups of stacks, and an “independence of $ℓ$ ” 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/

Vol. 6, No. 1, 2012