Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology, and Bohmann–Gerhardt–Høgenhaven–Shipley–Ziegenhagen developed a coBökstedt spectral sequence to compute the homology of \(\mathrm {coTHH}\) for coalgebras over the sphere spectrum. We construct a relative coBökstedt spectral sequence to study \(\mathrm {coTHH}\) of coalgebra spectra over any commutative ring spectrum R. Further, we use algebraic structures in this spectral sequence to complete some calculations of the homotopy groups of relative topological coHochschild homology.

中文翻译：

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相对拓扑coHochschild同调性的计算

Hess 和 Shipley 定义了称为拓扑 coHochschild 同调的余代数谱不变量，Bohmann-Gerhardt-Høgenhaven-Shipley-Ziegenhagen 开发了 coBökstedt 谱序列来计算球谱上余代数\(\mathrm {coTHH}\)的同源性。我们构造一个相对 coBökstedt 谱序列来研究任意交换环谱R上的余代数谱\(\mathrm {coTHH}\)。进一步，我们利用该谱序列中的代数结构来完成相对拓扑coHochschild同调的同伦群的一些计算。