\(L\)-series of Artin stacks over finite fields
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 \(L\left( X,K,s\right) \).
scientific article; zbMATH DE number 6064705