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

Bruno Kahn

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

Number Theory 2016-03-04 v3 Algebraic Geometry

Authors: Bruno Kahn

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 $A$ .

Keywords

abelian variety L-function function field motivic formula l-adic cohomology arithmetico-geometric invariants

Cite

@article{arxiv.1401.6847,
  title  = {A motivic formula for the L-function of an abelian variety over a function field},
  author = {Bruno Kahn},
  journal= {arXiv preprint arXiv:1401.6847},
  year   = {2016}
}

Comments

Substantially revised. In particular proofs in Section 2 are simplified and clarified, and the motivation for Section 7 is more detailed

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

Abstract

Keywords

Cite

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