Infinite class towers for function fields

2011/05/07 by Jing Long Hoelscher, Hoelscher, Jing
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1105.1440

openalex publication_date 2011/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives examples of function fields K₀ over a finite field \mathbbF_q of p power order ramified only at one finite regular prime over \mathbbF_q(t), which admit infinite Hilbert p-class field towers. Such a K₀ can be taken as an extension of a cyclotomic function field \mathbbF_q(t)(λ_\mathfrakp^m) for a certain regular prime \mathfrakp in \mathbbF_q[t].

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