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. |