JOURNAL ARTICLE

The Galois‐equivariant K‐theory of finite fields.

  • Published In: Proceedings of the London Mathematical Society, 2025, v. 130, n. 1. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Chan, David; Vogeli, Chase 3 of 3

Abstract

We compute the RO(G)$RO(G)$‐graded equivariant algebraic K$K$‐groups of a finite field with an action by its Galois group G$G$. Specifically, we show these K$K$‐groups split as the sum of an explicitly computable term and the well‐studied RO(G)$RO(G)$‐graded coefficient groups of the equivariant Eilenberg–MacLane spectrum HZ̲$H\underline{\mathbb {Z}}$. Our comparison between the equivariant K$K$‐theory spectrum and HZ̲$H\underline{\mathbb {Z}}$ further shows they share the same Tate spectra and geometric fixed point spectra. In the case where G$G$ has prime order, we provide an explicit presentation of the equivariant K$K$‐groups. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Proceedings of the London Mathematical Society. 2025/01, Vol. 130, Issue 1, p1
  • Document Type:Article
  • Subject Area:History
  • Publication Date:2025
  • ISSN:0024-6115
  • DOI:10.1112/plms.70012
  • Accession Number:183912365
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