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Functional Transcendence of Periods and the Geometric Andr\'e--Grothendieck Period Conjecture

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arxiv 2208.05182 v2 pith:S72A4SIP submitted 2022-08-10 math.AG math.NT

Ben Bakker , Jacob Tsimerman This is my paper · ORCID
classification math.AGmath.NT
keywords algebraicconjectureperiodproveandrax--schanuelfunctionalgeneralization
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We prove a functional transcendence theorem for the integrals of algebraic forms in families of algebraic varieties. This allows us to prove a geometric version of Andr\'e's generalization of the Grothendieck period conjecture, which we state using the formalism of Nori motives. More precisely, we prove a version of the Ax--Schanuel conjecture for the comparison between the flat and algebraic coordinates of an arbitrary admissible graded polarizable variation of integral mixed Hodge structures. This can be seen as a generalization of the recent Ax--Schanuel theorems of \cite{chiu,GaoKlingler} for mixed period maps.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A conjecture in Schanuel style for 1-motives

    math.NT 2025-09 conditional novelty 6.0 of 10

    A Schanuel-style algebraic independence conjecture for semi-elliptic exponentials is shown equivalent to the Grothendieck-André periods conjecture for 1-motives, with the CM torsion-point case proved.

  2. What makes an algebraic curve special?

    math.AG 2025-02 conditional novelty 3.0 of 10

    A survey of special curves and special subvarieties of moduli space, unifying Hodge-theoretic, Teichmüller, and bi-algebraic perspectives, with a few new results and conjectures.

  3. Hodge theory and o-minimality at CIRM

    math.AG 2025-02 unverdicted

    Survey lecture notes connecting o-minimality, Ax-Schanuel theorems, and the Zilber-Pink conjecture for Hodge loci, with no new results.

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