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The Tambara Structure of the Trace Ideal for Cyclic Extensions

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arxiv 1910.03029 v2 pith:SGOJ3R2O submitted 2019-09-30 math.NT math.ATmath.CTmath.GRmath.KT

Maxine Calle , Sam Ginnett , Harry Chen , Xinling Chen This is my paper · ORCID
classification math.NTmath.ATmath.CTmath.GRmath.KT
keywords idealtracecyclicextensionfinitetambaraextensionsfunctor
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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.

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