Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
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Orateur(s) S. Yasuda - ,
Titre Congruence and product formula for local constants
Date10/02/2003
Horaire14:00 à 16:00
RésumeThe theory of local $\epsilon$-factors is generalized in the followingway.Let $K$ be a complete discrete valuation field whose residue field$k$ is perfect ofpositive characteristic $p$. Let $W_K$ be the Weil group of $K$.For each triple $(R,(\rho,V),\psi)$, where $R$ is a noetherian localringwith algebraically closed residue field of characteristic $\neq p$such thatthe $p$-power map $R^{\times}\to R^{\times}$ is surjective,$(\rho,V)$ is a continuous representations of $W_K$ ona finitely generated free $R$-module $V$,and $\psi:K\to R^{\times}$ is a non-trivial additive charactersheaf, I defined the local $\epsilon_0$-character$\epsilon_{0,R}(V,\psi)$ of $(R,(\rho,V),\psi)$and discussed its basic properties. As applications,I generalized Deligne-Laumon's product formuladescribing the determinants of cohomologies of$l$-adic etale sheaves on curves over finite fields,and Saito's formula for describing the determinants of cohomologiesoftamely ramified $l$-adic etale sheaves on varieties over finite fields,to the case of $\Lambda$-sheaves for pro-finite rings $\Lambda$.
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