Vol. 6, No. 1, 2021

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The topological Hochschild homology of algebraic $K\mkern-2mu$-theory of finite fields

Eva Höning

Vol. 6 (2021), No. 1, 29–96

Let K(𝔽q) be the algebraic K-theory spectrum of the finite field with q elements and let p 5 be a prime number coprime to q. We study the mod p and v1 topological Hochschild homology of K(𝔽q), denoted V (1)THH(K(𝔽q)), as an 𝔽p-algebra. The computations are organized in four different cases, depending on the p-adic behavior of the function qn 1. We use several different spectral sequences, in particular the Bökstedt spectral sequence and a generalization of a spectral sequence of Brun developed in an earlier paper. We calculate the 𝔽p-algebra THH(K(𝔽q);H𝔽p), and we compute V (1)THH(K(𝔽q)) in the first two cases.

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topological Hochschild homology, algebraic $K\mkern-2mu$-theory
Mathematical Subject Classification
Primary: 19D55, 55P42
Received: 16 August 2019
Revised: 7 August 2020
Accepted: 23 August 2020
Published: 8 July 2021
Eva Höning
Department of Mathematics
Radboud University
The Netherlands