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Notes on Motives in Finite Characteristic

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Algebra, Arithmetic, and Geometry

Part of the book series: Progress in Mathematics ((PM,volume 270))

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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Author information

Authors and Affiliations

  1. IHES, 35 route de Chartres, Bures-sur-Yvette, 91440, France

    Maxim Kontsevich

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  1. Maxim Kontsevich
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Correspondence to Maxim Kontsevich .

Editor information

Editors and Affiliations

  1. Courant Inst. Mathematical, New York University, Mercer St. 251, New York, 10012, USA

    Yuri Tschinkel

  2. Eberly College of Science, Pennsylvania State University, University Park, 16802, USA

    Yuri Zarhin

Additional information

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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