The Tambara Structure of the Trace Ideal for Cyclic Extensions

This paper explores the Tambara functor structure of the trace ideal of a Galois extension. In the case of a (pro-)cyclic extension, we are able to explicitly determine the generators of the ideal. Furthermore, we show that the absolute trace ideal of a cyclic group is strongly principal when viewed...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-05
Main Authors: Calle, Maxine, Ginnett, Sam, Chen, Harry, Chen, Xinling
Format: Article
Language:English
Subjects:
Fields (mathematics)
Quadratic forms
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper explores the Tambara functor structure of the trace ideal of a Galois extension. In the case of a (pro-)cyclic extension, we are able to explicitly determine the generators of the ideal. Furthermore, we show that the absolute trace ideal of a cyclic group is strongly principal when viewed as an ideal of the Burnside Tambara Functor. Applying our results, we calculate the trace ideal for extensions of finite fields. The appendix determines a formula for the norm of a quadratic form over an arbitrary finite extension of a finite field.
ISSN:2331-8422
DOI:10.48550/arxiv.1910.03029