Periods of the motivic fundamental groupoid of \boldsymbolℙ¹ \diagdown \lbrace 0, μ_N, ∞ \rbrace

2016/03/16 by Claire Glanois, Glanois, Claire · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1603.05155

openalex publication_date 2016/03/16 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this thesis, following F. Brown's point of view, we look at the Hopf algebra structure of motivic cyclotomic multiple zeta values, which are motivic periods of the fundamental groupoid of ℙ¹ \diagdown \lbrace 0, μ_N, ∞ \rbrace . By application of a surjective period map (which, under Grothendieck's period conjecture, is an isomorphism), we deduce results (such as generating families, identities, etc.) on cyclotomic multiple zeta values, which are complex numbers. The coaction of this Hopf algebra (explicitly given by a combinatorial formula from A. Goncharov and F. Brown's works) is the dual of the action of a so-called motivic Galois group on these specific motivic periods. This entire study was actually motivated by the hope of a Galois theory for periods, which should extend the usual Galois theory for algebraic numbers.

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