References & Citations
Mathematics > Number Theory
Title: Extended genus fields of abelian extensions of rational function fields
(Submitted on 26 Apr 2024)
Abstract: In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. Next, we use that the extended genus fields of a composite of two cyclotomic extensions of a global rational function field is equal to the composite of their respective extended genus fields, to obtain our main result. This result is that the extended genus field of a general finite abelian extension of a global rational function field, is given explicitly in terms of the field and of the extended genus field of its "cyclotomic projection".
Submission history
From: Gabriel Villa-Salvador [view email][v1] Fri, 26 Apr 2024 17:51:05 GMT (20kb)
Link back to: arXiv, form interface, contact.