2022/07/05 by Bryden Cais, Cais, Bryden
Arts and Humanities · Mathematics · #11R23 (Primary) #11R58 #14H30 (Secondary) #14L05 #14L15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2207.02283
openalex publication_date 2022/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be a perfect field of characteristic p and Γ an infinite, first countable pro-p group. We study the behavior of the p-primary part of the "motivic class group", i.e. the full p-divisible group of the Jacobian, in any Γ-tower of function fields over k that is unramified outside a finite (possibly empty) set of places Σ, and totally ramified at every place of Σ. When Σ=∅ and Γ is a torsion free p-adic Lie group, we obtain asymptotic formulae which show that the p-torsion class group schemes grow in a remarkably regular manner. In the ramified setting Σ≠∅, we obtain a similar asymptotic formula for the p-torsion in "physical class groups", i.e. the k-rational points of the Jacobian, which generalizes the work of Mazur and Wiles, who studied the case Γ=Zp.