Groupes de Galois motivques et p\'eriodes
Yves Andr\'e

TL;DR
This paper discusses the development of motivic Galois theory, connecting it to periods of algebraic varieties and showing that relations between periods originate from Stokes' formula, advancing understanding of algebraic and motivic structures.
Contribution
It introduces a new tannakian approach based on Voevodsky's mixed motives, providing deeper insights into periods and their relations in algebraic geometry.
Findings
Relations between periods arise from Stokes' formula
Voevodsky's theory underpins the new tannakian approach
Advances understanding of motivic Galois groups
Abstract
In the mid sixties, A. Grothendieck envisioned a vast generalization of Galois theory to systems of polynomials in several variables, motivic Galois theory, and introduced tannakian categories on this occasion. In characteristic zero, various unconditional approaches were later proposed. The most precise one, due to J. Ayoub, relies on Voevodsky theory of mixed motives and on a new tannakian theory. It sheds new light on periods of algebraic varieties, and shows in particular that polynomial relations between periods of a pencil of algebraic varieties always arise from Stokes formula.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Commutative Algebra and Its Applications
