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arXiv · 1401.6847

A motivic formula for the L-function of an abelian variety over a function field

Bruno Kahn
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Abstract

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 $H^1(\bar A,\mathbf{Q}_l)$ 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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Bruno Kahn. 2016-03-03. A motivic formula for the L-function of an abelian variety over a function field. https://arxiv.org/abs/1401.6847

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