发表机构
Institute of Mathematics, Czech Academy of Sciences（捷克科学院数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
将BMS动机滤过推广至Azumaya代数，证明其THH等价于中心的THH（经约化迹归一化），并建立étale局部循环同调性质，滤过不依赖Brauer类。
AI 中文摘要
Bhatt-Morrow-Scholze在拓扑Hochschild同调（$THH$）上的动机滤过被推广到拟合成环上的Azumaya代数。我们证明了Azumaya下降定理：此类代数的$THH$，作为底层谱，等价于其中心的$THH$，但在$\u03c0_0$上通过约化迹而非单位映射进行归一化。此比较$\u03a6_A$未被证明是étale局部循环同调的。但在étale局部上是循环同调的是一个独立的Morita迹，仅在$\u03c0_0$上与$\u03a6_A$一致。由此得到的传输滤过恰好是中心的BMS滤过，在$\u03a6_A$的自同构歧义下定义良好。它不依赖于Brauer类，而Brauer类反映在$K$理论和模范畴配对中，这些是$THH$所无法察觉的。我们在连通性假设下，对连通$\u211d_\u221e$-环上的导出Azumaya代数建立了类似结论。
英文摘要
Bhatt-Morrow-Scholze motivic filtration on topological Hochschild homology ($THH$) is extended to Azumaya algebras over quasisyntomic rings. We prove the Azumaya descent theorem: $THH$ of such an algebra is equivalent, as an underlying spectrum, to $THH$ of its center, normalized on $π_0$ by the reduced trace instead of the unit map. This comparison $Φ_A$ is not shown to be étale-locally cyclotomic. But what is cyclotomic étale-locally is a separate Morita trace, agreeing with $Φ_A$ only on $π_0$. The resulting transported filtration is exactly the center BMS filtration, well defined up to the automorphism ambiguity of $Φ_A$. It is insensitive to the Brauer class, reflected instead by $K$-theoretic and module-categorical pairings $THH$ does not see. We establish the analogous statement for derived Azumaya algebras over connective $\mathbb{E}_\infty$-rings, under a connectivity hypothesis.
