On the relationship between logarithmic TAQ and logarithmic THH

Logarithmic topological Hochschild homology of topological K-theory spectra

In this paper we continue our study of logarithmic topological Hochschild homology. We show that the inclusion of the connective Adams summand into the p-local complex connective K-theory spectrum, equipped with suitable log structures, is a formally log THH-etale map, and compute the V(1)-homotopy of their logarithmic topological Hochschild homology spectra. As an application, we recover Ausoni's computation of the V(1)-homotopy of the ordinary THH of ku.

论对数拓扑循环同调中的留数序列

On the Residue Sequence in Logarithmic Topological Cyclic Homology

本研究通过关联循环谱局部化序列与对数THH留数序列解决Rognes猜想，证明对数THH、TR、TC是相关构造的严格推广且无需正则假设即可有局部化序列，结合已有工作证明存在稳定无穷范畴实现特定对数结构的对数项，并提出该范畴可反映额外结构的猜想及离散赋值环情形的证据。

高度二截断Brown-Peterson谱的对数拓扑Hochschild同调

Logarithmic topological Hochschild homology of the truncated Brown--Peterson spectrum

研究截断Brown-Peterson谱BP{n}的对数拓扑Hochschild同调，通过预对数结构和谱序列分析，计算了n=2时V(2)-同伦群。

根的附加，代数 $K$-理论与色散红移

Adjunction of roots, algebraic $K$-theory and chromatic redshift

本文定义了 $E_1$-环的根附加和对数 THH，证明了根附加在代数 $K$-理论中诱导楔直和项的包含，并利用此结果证明了 Lubin-Tate 谱满足色散红移猜想。

对数拓扑循环同调性的局部化序列

Localization sequences for logarithmic topological cyclic homology

引入具有预对数结构的E_k-环，定义对数拓扑Hochschild同调和对数拓扑循环同调，并建立这些理论的局部化序列，基于Thom R-代数，扩展并加强了先前工作。