Function field genus theory for non-Kummer extensions
Martha Rzedowski-Calder\'on, Gabriel Villa-Salvador
TL;DR
This paper develops a comprehensive theory for the genus field of finite abelian non-Kummer extensions over global rational function fields, extending previous results to a general setting.
Contribution
It provides a general formula for the genus field of any finite abelian extension of a global rational function field, including non-Kummer cases.
Findings
Derived the genus field for non-Kummer abelian extensions.
Showed the genus field of a composite of extensions equals the composite of their genus fields.
Extended genus field theory to broader classes of function field extensions.
Abstract
In this paper we first obtain the genus field of a finite abelian non-Kummer --extension of a global rational function field. Then, using that the genus field of a composite of two abelian extensions of a global rational function field with relatively prime degrees is equal to the composite of their respective genus fields and our previous results, we deduce the general expression of the genus field of a finite abelian extension of a global rational function field.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · African history and culture studies · Algebraic Geometry and Number Theory