Algebraicity of Artin--Hasse--Weil L-series over global function fields

TL;DR

This paper proves an analogue of Deligne's period conjecture for special L-values of abelian varieties over global function fields twisted by Artin representations, with an example involving an elliptic curve and Dirichlet characters.

Contribution

It establishes a new period conjecture analogue for L-functions over function fields, extending Deligne's conjecture to this setting.

Findings

Proved the analogue of Deligne's period conjecture for abelian varieties over function fields.

Demonstrated the theory with an elliptic curve twisted by a Dirichlet character.

Provided explicit calculations illustrating the main results.

Abstract

We prove an analogue of Deligne's period conjecture for the special value of the L-function of an abelian variety over a global function field twisted by an Artin representation. We illustrate this in action for an example of an elliptic curve twisted by a Dirichlet character.