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$𝒟$ -modules arithmétiques surcohérents. Application aux fonctions $L$

Daniel Caro (2004)

Annales de l’institut Fourier

Nous étudions d’abord le foncteur cohomologique local. Ensuite, nous introduisons la notion de $𝒟$ -modules arithmétiques surcohérents. Nous prouvons que les $F$ - 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 $L$ associées aux complexes duaux de complexes surcohérents. Celle-ci étend celle d’Étesse et Le Stum...

A Classical Diophantine Problem and Modular Forms of Weight 3/2.

J.B. Tunnell (1983)

Inventiones mathematicae

A counterexample in the theory of local zeta functions.

Martin, Roland (1995)

Experimental Mathematics

A Gauss-Bonnet theorem for motivic cohomology.

S. Turner (1990)

Inventiones mathematicae

A motivic Chebotarev density theorem.

Dhillon, Ajneet, Mináč, Ján (2006)

The New York Journal of Mathematics [electronic only]

A new construction of $p$ -adic $L$ -functions attached to certain elliptic curves with complex multiplication

John L. Boxall (1986)

Annales de l'institut Fourier

In this paper we apply the results of our previous article on the $p$ -adic interpolation of logarithmic derivatives of formal groups to the construction of $p$ -adic $L$ -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.

A note on functional equations for zeta functions with values in Chow motives

Franziska Heinloth (2007)

Annales de l’institut Fourier

We consider zeta functions with values in the Grothendieck ring of Chow motives. Investigating the $λ$ –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.