Summary
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 in statistical physics.
2000 Mathematics Subject Classifications: 11G25, 37K20, 37C30, 11R39, 82B20, 18D05
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To Yuri Manin on the occasion of his 70th birthday, with admiration
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Kontsevich, M. (2009). Notes on Motives in Finite Characteristic. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 270. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4747-6_7
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DOI: https://doi.org/10.1007/978-0-8176-4747-6_7
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