𝐻(ℤ/𝕡^{𝕜}) as a Thom spectrum and topological Hochschild homology

Kitchloo, Nitu

doi:10.1090/proc/14968

$\operatorname {H}(\mathbb {Z}/p^k)$ as a Thom spectrum and topological Hochschild homology
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Proc. Amer. Math. Soc. 148 (2020), 3647-3651 Request permission

Abstract:

In this short note we study the topological Hochschild homology of Eilenberg-MacLane spectra for finite cyclic groups. In particular, we show that the Eilenberg-MacLane spectrum $\operatorname {H}(\mathbb {Z}/p^k)$ is a Thom spectrum for any prime $p$ (except, possibly, when $p=k=2$) and we also compute its topological Hoschshild homology. This yields a short proof of the results obtained by Brun [J. Pure Appl. Algebra 148 (2000), pp. 29–76], and Pirashvili [Comm. Algebra 23 (1995), pp. 1545–1549] except for the anomalous case $p=k=2$.

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