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This is a Quantitative Study study.

October 7, 2025Open Access

On Andr\'e periods of mixed Tate motives

Key Points

Andr periods of mixed Tate motives equate to classical notions in this setting, enhancing understanding.
The study connects Andr periods with p-adic integration techniques, bridging modern and classical methods.
Frobenius-fixed de Rham paths can be derived from motivic paths in characteristic p, expanding theoretical applications.
Special values of p-adic multiple polylogarithms can be concretely realized as Andr periods, highlighting their significance.

Abstract

In this note, we show that the p-adic periods of motives introduced recently by Ancona and Fratila (``Andr\'e periods'') reduce to the classically studied notion in the case of Mixed Tate motives. We also connect Andr\'e periods with Coleman integration by observing that the Frobenius-fixed de Rham paths of Besser and Vologodsky come from motivic paths in characteristic p (unconditionally in the mixed Tate setting, conditionally in general). We use this to realize special values of p-adic multiple polylogarithms as Andr\'e periods in a concrete way.

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Cite This Study

Ishai Dan-Cohen (Mon,) studied this question.

synapsesocial.com/papers/68e585d0b1e78cc4e5f463d4 https://doi.org/https://doi.org/10.48550/arxiv.2502.17404

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