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structured ring spectrum

Journal of the Institute of Mathematics of Jussieu (1)

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GENERALIZED THOM SPECTRA AND THEIR TOPOLOGICAL HOCHSCHILD HOMOLOGY
Part of
Samik Basu, Steffen Sagave, Christian Schlichtkrull
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 1 / January 2020

Published online by Cambridge University Press:

02 November 2017, pp. 21-64

Print publication:

January 2020
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We develop a theory of $R$-module Thom spectra for a commutative symmetric ring spectrum $R$ and we analyze their multiplicative properties. As an interesting source of examples, we show that $R$-algebra Thom spectra associated to the special unitary groups can be described in terms of quotient constructions on $R$. We apply the general theory to obtain a description of the $R$-based topological Hochschild homology associated to an $R$-algebra Thom spectrum.