The Tambara Structure of the Trace Ideal for Cyclic Extensions
Number Theory
2024-03-08 v2 Algebraic Topology
Category Theory
Group Theory
K-Theory and Homology
Abstract
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.
Keywords
Cite
@article{arxiv.1910.03029,
title = {The Tambara Structure of the Trace Ideal for Cyclic Extensions},
author = {Maxine Calle and Sam Ginnett and Harry Chen and Xinling Chen},
journal= {arXiv preprint arXiv:1910.03029},
year = {2024}
}
Comments
25 pages, comments welcome. This version is the pre-proof of the article published in the Journal of Algebra