Notes on motives in finite characteristic

Abstract

Motivic local systems over a curve in finite characteristic form a countable set endowed with an action of the absolute Galois group of rational numbers commuting with the Frobenius map. I will discuss three series of conjectures about such sets, based on an analogy with algebraic dynamics, on a formalism of commutative algebras of motivic integral operators, and on an analogy with 2-dimensional lattice models.