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.

中文翻译：

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广义 THOM 谱及其拓扑 Hochschild 同源性

我们开发了一个理论$R$交换对称环谱的模 Thom 谱$R$我们分析它们的乘法性质。作为一个有趣的例子来源，我们表明$R$- 与特殊酉群相关的代数 Thom 谱可以用商结构来描述$R$. 我们应用一般理论来获得对$R$基于拓扑的 Hochschild 同源性与$R$-代数 Thom 谱。