The Tambara structure of the trace ideal for cyclic extensions

JOURNAL OF ALGEBRA

卷:560

Article

关键词: Trace ideal;    Burnside ring;    Grothendieck-Witt ring;    Tambara functor;    Mackey functor;    Scharlau transfer;    Rost norm;   

DOI  :  10.1016/j.jalgebra.2020.04.036

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free