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Theses

Motivic cohomology in the arithmetic of function fields

Abstract : The deepest arithmetic invariants attached to an algebraic variety defined over a number field are conjecturally captured by its so-called motivic cohomology. Values of L-functions and K-groups of varieties are some examples. This thesis describes the analogous picture for global fields in equal characteristic. The main objective is to compute the extension modules in various categories of Anderson A-motives and to prove a finiteness theorem. We conclude with a discussion on Beilinson’s first conjecture in function fields arithmetic. Finally, we explain how our results apply to investigate algebraic relations among values of Carlitz polylogarithms.
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https://hal.archives-ouvertes.fr/tel-03439317
Contributor : Quentin Gazda Connect in order to contact the contributor
Submitted on : Monday, November 22, 2021 - 11:06:19 AM
Last modification on : Saturday, November 27, 2021 - 3:48:54 AM
Long-term archiving on: : Wednesday, February 23, 2022 - 6:35:22 PM

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  • HAL Id : tel-03439317, version 1

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Quentin Gazda. Motivic cohomology in the arithmetic of function fields. Number Theory [math.NT]. Université Jean Monnet, 2021. English. ⟨tel-03439317⟩

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