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arXiv · 2602.21894

The cyclosyntomic regulator of a number field

Tess Bouis·Quentin Gazda
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Abstract

We construct a q-deformation of the p-adic regulator of a number field, called the cyclosyntomic regulator, building on the Habiro ring of Garoufalidis-Scholze-Wheeler-Zagier. The key new ingredient in our construction is a refinement of Sulyma's norm maps in prismatic cohomology, which interpolate between classical powers and Frobenius maps at various prime numbers p. Furthermore, we compute the values of the cyclosyntomic regulator at units of the form $1-\zeta$, where $\zeta$ is a root of unity.

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Tess Bouis, Quentin Gazda. 2026-02-25. The cyclosyntomic regulator of a number field. https://arxiv.org/abs/2602.21894

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