Annihilators of the ideal class group of a cyclic extension of a global function field

2020/11/17 by Pascal Stucky, Stucky, Pascal
Mathematics · #11G09 (Secondary) #11R20 #11R58 (Primary) 11R27 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G09 #msc:11R20 #msc:11R27 #msc:11R58

paper · pdf · doi:10.48550/arxiv.2011.08776

31 pages

arxiv created 2020/11/17 · openalex publication_date 2020/11/17 · arxiv updated 2020/11/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let K be a global function field and fix a place ∞ of K. Let L/K be a finite real abelian extension, i.e. a finite, abelian extension such that ∞ splits completely in L. Then we define a group of elliptic units C_L in O_L^× analogously to Sinnott's cyclotomic units and compute the index [O_L^×:C_L]. In the second part of this article, we additionally assume that L is a cyclic extension of prime power degree. Then we can use the methods from Greither and Kučera to take certain roots of these elliptic units and prove a result on the annihilation of the p-part of the class group of L.

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