Class Group Relations in a Function Field Analogue of \mathbb Q(ζ_p, √[p]n)

2020/11/17 by Steven Reich, Reich, Steven
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2011.08640

openalex publication_date 2020/11/17 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

For an odd prime p and polynomial P(T), we consider the extension F of k=\mathbb F_p(T) defined by adjoining a root of x^p+Tx-P(T). Such a field is a function field analogue of the number field \mathbb Q(√[p]n). We prove two theorems about the Galois closure L of F: that its degree-0 divisor class group is A^p-1 for some group A, and that its class number is the (p-1)-st power of the class number of F, in analogy with results of R. Schoof and T. Honda for number fields.

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