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arXiv · 1810.11941

Category Of C-Motives Over Finite Fields

Eamail Arasteh Rad·Urs Hartl
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Abstract

In this article we introduce and study a motivic category in the arithmetic of function fields, namely the category of motives over an algebraic closure $L$ of a finite field with coefficients in a global function field over this finite field. It is semi-simple, non-neutral Tannakian and possesses all the expected fiber functors. This category generalizes the previous construction due to Anderson and is more relevant for applications to the theory of $G$-Shtukas, such as formulating the analog of the Langlands-Rapoport conjecture over function fields. We further develop the analogy with the category of motives over $L$ with coefficients in $\mathbb{Q}$ for which the existence of the expected fiber functors depends on famous unproven conjectures.

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BibTeXRIS

Eamail Arasteh Rad, Urs Hartl. 2020-09-30. Category Of C-Motives Over Finite Fields. https://doi.org/10.1016/j.jnt.2020.06.015

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