2025/12/12 by Roset, Martí, Xu, Peter
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Advanced Algebra and Geometry
paper · doi:10.48550/arxiv.2512.11514
Starting from a topological treatment of the Eisenstein class of a torus bundle, we define log-rigid analytic classes for SLn(ℤ). These are group cohomology classes for SLn(ℤ) valued on log-rigid analytic functions on Drinfeld's p-adic symmetric domain. Such classes can be evaluated at points attached to totally real fields of degree n where p is inert. We conjecture that these values are p-adic logarithms of Gross--Stark units in the narrow Hilbert class field of totally real fields. We provide evidence for the conjecture by comparing our constructions to p-adic L-functions. In addition, we prove it in certain situations where the totally real field is Galois over ℚ, as a consequence of the fact that in this case there is a conjugate of a Gross--Stark unit in ℚp.