The cyclosyntomic regulator of a number field
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 $1-ζ$, where $ζ$ is a root of unity.
Fields of Study & Subjects
Advanced Algebra and Geometry
Advanced Mathematical Identities
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 25 February 2026
- Language
- EN
- Document type
- Preprint