Motivic p-adic periods of 1-motives

Felix Sefzig

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arXiv · 2510.20525

Motivic p-adic periods of 1-motives

Felix Sefzig

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Abstract

We give an explicit construction of the p-adic de Rham comparison isomorphism for 1-motives. In particular, we prove that our construction recovers the classical de Rham comparison isomorphism and is functorial with respect to morphisms of rigid 1-motives. In the second part, we construct a new ring of motivic p-adic periods using the formalism of rigid analytic motives. Furthermore, we explain the relation between these motivic periods and the periods of the classical p-adic de Rham comparison isomorphism. Finally, we apply our construction to explicitly compute the period pairing for several examples of 1-motives and curves.

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Felix Sefzig. 2025-10-23. Motivic p-adic periods of 1-motives. https://arxiv.org/abs/2510.20525

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