Finite generation and continuity of topological Hochschild and cyclic homology

B. Dundas, M. Morrow
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引用次数: 10

Abstract

The goal of this paper is to establish fundamental properties of the Hochschild, topological Hochschild, and topological cyclic homologies of commutative, Noetherian rings, which are assumed only to be F-finite in the majority of our results. This mild hypothesis is satisfied in all cases of interest in finite and mixed characteristic algebraic geometry. We prove firstly that the topological Hochschild homology groups, and the homotopy groups of the fixed point spectra $TR^r$, are finitely generated modules. We use this to establish the continuity of these homology theories for any given ideal. A consequence of such continuity results is the pro Hochschild-Kostant-Rosenberg theorem for topological Hochschild and cyclic homology. Finally, we show more generally that the aforementioned finite generation and continuity properties remain true for any proper scheme over such a ring.
拓扑Hochschild与循环同调的有限生成与连续性
本文的目的是建立交换Noetherian环的Hochschild,拓扑Hochschild和拓扑循环同调的基本性质,在我们的大多数结果中只假设它们是f有限的。这个温和的假设在有限和混合特征代数几何的所有情况下都得到满足。首先证明了拓扑Hochschild同伦群和不动点谱$TR^r$的同伦群是有限生成模。我们用它来建立这些同调理论对任何给定理想的连续性。这种连续性结果的一个推论是拓扑Hochschild和循环同调的亲Hochschild- kostant - rosenberg定理。最后,我们更普遍地证明了上述有限生成和连续性质对这样一个环上的任何适当格式都成立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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