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Notes on motives in finite characteristic

Maxim Kontsevich
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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.

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Maxim Kontsevich. 2007-05-30. Notes on motives in finite characteristic. https://arxiv.org/abs/math/0702206

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