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) Matthias Flach - ,
Titre Weil-etale cohomology and Zeta functions of arithmetic schemes
Date28/02/2011
Horaire14:00 à 16:00
Résume We discuss the conjectural description of leading Taylor coefficients of Zetafunctions of arithmetic schemes at integer arguments in terms of Weil-etalecohomology groups, expanding on ideas of Lichtenbaum. We then describe joint workwith Baptiste Morin in which we define a Weil-etale topos of a regular arithmeticscheme whose cohomology with R-coefficients has the expected relation to theZeta-function under standard assumptions on Hasse-Weil L-functions (satisfied forexample for regular models of powers of an elliptic curve over a totally realfield). Finally we discuss compatibility of this picture with the Tamagawa numberconjecture of Bloch, Kato, Fontaine and Perrin-Riou.
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