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Nous étudions d’abord le foncteur cohomologique local. Ensuite, nous introduisons la
notion de -modules arithmétiques surcohérents. Nous prouvons que les -
isocristaux unités sont surcohérents et surtout que la surcohérence est stable par images
directes, images inverses extraordinaires et foncteurs cohomologiques locaux. On obtient,
via cette stabilité, une formule cohomologique pour les fonctions associées aux
complexes duaux de complexes surcohérents. Celle-ci étend celle d’Étesse et Le Stum...
In this paper we apply the results of our previous article on the -adic interpolation of logarithmic derivatives of formal groups to the construction of -adic -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.
We consider zeta functions with values in the Grothendieck ring of Chow motives. Investigating the –structure of this ring, we deduce a functional equation for the zeta function of abelian varieties. Furthermore, we show that the property of having a rational zeta function satisfying a functional equation is preserved under products.
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