论文标题
解开相对泰特对角线
Unwinding the relative Tate diagonal
论文作者
论文摘要
我们表明，Lipshitz和Treumann开发的光谱序列应用于Heegaard浮子理论，将其收敛到具有系数的拓扑Hochschild同源性的局部形式。这使我们能够证明，当拓扑序列同源性时，当拓扑序列的目标可以通过$ \ mathrm {thh} _*（\ Mathbb {f} _2）$（平行于Mathew of Mathew of Mathew of Mathew of Mathew of Mathew of Mathew of Mathew of Mathew of Mathew of Mathew of Mathew of Mathew of hodge toge toge rham speceperral of hodepe rhamspecy rhamspecy rham rham rham rham，hochschild同源性的目标无扭转。为了执行此操作，我们应用了Nikolaus-Scholze的工作，以开发一般的泰特对角线，用于像Hochschild的光谱图，尊重分解为张量产品。这使我们能够讨论相对拓扑Hochschild同源性的泰特对角线的程度。
We show that a spectral sequence developed by Lipshitz and Treumann, for application to Heegaard Floer theory, converges to a localized form of topological Hochschild homology with coefficients. This allows us to show that the target of this spectral sequence can be identified with Hochschild homology when the topological Hochschild homology is torsion-free as a module over $\mathrm{THH}_*(\mathbb{F}_2)$, parallel to results of Mathew on degeneration of the Hodge-to-de Rham spectral sequence. To carry this out, we apply work of Nikolaus-Scholze to develop a general Tate diagonal for Hochschild-like diagrams of spectra that respect a decomposition into tensor products. This allows us to discuss the extent to which there can be a Tate diagonal for relative topological Hochschild homology.
