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Dimension formulas for period spaces via motives and species

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arxiv 2405.21053 v2 pith:RCTKCKTG submitted 2024-05-31 math.NT math.RAmath.RT

Annette Huber , Martin Kalck This is my paper · ORCID
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keywords dimensionnumbersalgebraiccaseciteformulasmotivesperiod
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abstract

We apply the structure theory of finite dimensional algebras in order to deduce dimension formulas for spaces of period numbers, i.e., complex numbers defined by integrals of algebraic nature. We get a complete and conceptually clear answer in the case of $1$-periods, generalising classical results like Baker's theorem on the logarithms of algebraic numbers and partial results in Huber--W{\"u}stholz \cite{huber-wuestholz}. The application to the case of Mixed Tate Motives (i.e., Multiple Zeta Values) recovers the dimension estimates of Deligne--Goncharov \cite{deligne-goncharov}.

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