Category Of C-Motives Over Finite Fields

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.

References in corpus (3)

• Local Models For The Moduli Stacks of Global $G$-Shtukas
• Langlands-Rapoport Conjecture Over Function Fields
• Rapoport-Zink Spaces For Local P-Shtukas and Their Local Models

Cited by in corpus (2)

• Rapoport-Zink Spaces For Local P-Shtukas and Their Local Models
• A Note On Two Fiber Bundles and The Manifestations Of "Shtuka"