# Séminaires : Séminaire Théorie des Nombres

 Equipe(s) : fa, tn, tga, Responsables : Marc Hindry, Bruno Kahn, Wieslawa Niziol, Cathy Swaenepoel Email des responsables : cathy.swaenepoel@imj-prg.fr Salle : Adresse : Description http://www.imj-prg.fr/tn/STN/stnj.html

 Orateur(s) S. Yasuda - , Titre Congruence and product formula for local constants Date 10/02/2003 Horaire 14:00 à 16:00 Diffusion Résume The 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 $\Lambda$. Salle Adresse