Mixed Tate motives over \Z

2011/02/07 by Brown, Francis · 9 citations
#11M32 #20F34 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1102.1312

Abstract

We prove that the category of mixed Tate motives over \Z is spanned by the motivic fundamental group of \Pro¹ minus three points. We prove a conjecture by M. Hoffman which states that every multiple zeta value is a \Q-linear combination of ζ(n₁,..., n_r) where n_i∈ \2,3\.

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• Unramified Motivic Multiple Mixed Values
• On the Problem of Mixed-Tateness of the Motives of G-Varieties
• The motivic Galois group for a double zeta value
• A Lie algebra associated with adjoint multiple zeta values
• Double shuffle relations imply the infinitesimal hexagon equation
• Derivative sums of balanced gamma quotients and multiple zeta values: four conjectures of Zhi-Wei Sun
• Towards Motivic Coactions at Genus One from Zeta Generators
• Solving Infinite Families of Dual Conformal Integrals and Periods

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• The motivic Galois group for a double zeta value
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• Algebraic cycles and motivic iterated integrals II