\(L\)-series of Artin stacks over finite fields
type: Item
instance of: scholarly article
title: \(L\)-series of Artin stacks over finite fields
zbMATH Open document ID: 1329.14042
author: Shenghao Sun
published in: Algebra \& Number Theory
publication date: 2012-08-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1008.3689
reviewed by: Feng-Wen An
Mathematics Subject Classification ID: 14F20
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 19F27
zbMATH DE Number: 6064705
zbMATH Keywords: \(\ell\)-adic cohomology
zbMATH Keywords: algebraic stack
zbMATH Keywords: operations on stack
zbMATH Keywords: \(L\)-series of stack
zbMATH Keywords: trace formula
MaRDI profile type: Publication
OpenAlex ID: W2066916156
arXiv ID: 1008.3689
Wikidata QID: Q57277703
DOI: 10.2140/ANT.2012.6.47
review text: For an \(\mathbb{F}_{q}\)-algebraic stack \(X\) and a stratifiable Weil complex \( K\) of sheaves on \(X\), one has an \(L\)-series \(L\left( X,K,s\right) \) attached to them, i.e., a formal power series of \(s\) constructed by traces of Frobenius maps. Now consider a morphism \(f:X\rightarrow Y\) of \(\mathbb{F}_{q} \)-algebraic stacks.NEWLINENEWLINEIn this paper the author proves the main result that the two attached \(L\) -series \(L\left( X,K,s\right) =L\left( Y,f_{!}K,s\right) \) are equal. He also obtains the analytic continuation and infinite product for the \(L\) -series \(L\left( X,K,s\right) \).
description: scientific article; zbMATH DE number 6064705