A motivic formula for the L-function of an abelian variety over a function field
Résumé
Let A be an abelian variety over the function field of a smooth projective curve C over an algebraically closed field k. We compute the l-adic cohomology groups of C with coefficients in the locally constant sheaf associated to H^1(\bar A,Q_l) in terms of arithmetico-geometric invariants of A. We apply this, when k is the algebraic closure of a finite field, to a motivic computation of the L-function of A.
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