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- W2964203914 abstract "Let $R$ be an $E_infty$-ring spectrum. Given a map $zeta$ from a space $X$ to $BGL_1R$, one can construct a Thom spectrum, $X^zeta$, which generalises the classical notion of Thom spectrum for spherical fibrations in the case $R=S^0$, the sphere spectrum. If $X$ is a loop space ($simeq Omega Y$) and $zeta$ is homotopy equivalent to $Omega f$ for a map $f$ from $Y$ to $B^2GL_1R$, then the Thom spectrum has an $A_infty$-ring structure. The Topological Hochschild Homology of these $A_infty$-ring spectra is equivalent to the Thom spectrum of a map out of the free loop space of $Y$. This paper considers the case $X=S^1$, $R=K_p^wedge$, the p-adic $K$-theory spectrum, and $zeta = 1-p in pi_1BGL_1K_p^wedge$. The associated Thom spectrum $(S^1)^zeta$ is equivalent to the mod p $K$-theory spectrum $K/p$. The map $zeta$ is homotopy equivalent to a loop map, so the Thom spectrum has an $A_infty$-ring structure. I will compute $pi_*THH^{K_p^wedge}(K/p)$ using its description as a Thom spectrum." @default.
- W2964203914 created "2019-07-30" @default.
- W2964203914 creator A5056774275 @default.
- W2964203914 date "2017-01-01" @default.
- W2964203914 modified "2023-10-16" @default.
- W2964203914 title "Topological Hochschild homology of $K/p$ as a $K_p^wedge$ module" @default.
- W2964203914 doi "https://doi.org/10.4310/hha.2017.v19.n1.a13" @default.
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