Gorenstein duality for topological Hochschild homology and its real form.

拓扑 Hochschild 同调的 Gorenstein 对偶性及其真实形式。

• 批准号: 2606242
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2606242
• 关键词: Gorenstein; duality; topological; Hochschild; homology

The nicest sort of commutative rings are the regular local rings (not far from polynomial rings), and then those obtained from these by factoring out a regular sequence. However, the class of Gorenstein rings is much more general and famously (after Bass) ubiquitous. It turns out that this is also true for rings up to homotopy, and Greenlees shown that THH(R;k) is Gorenstein when R is regular local ring with residue field k of characteristic p. The project is to extend this result in two directions. Firstly, one expects it is true when R is Gorenstein (and not just regular), which would enormously enrich the range of examples. Secondly, it appears that a richer equivariant version applies to real THH when R has an anti-involution; this involves combining the above work with work of Dotto and Patchkoria and also work Greenlees with Meier on Gorenstein duality for BPR. In the course of doing this, a number of interesting spectral sequences will be developed which will be useful for explicit calculation.

最好的交换环是正则局部环(离多项式环不远)，然后从这些局部环中分解出一个正则序列得到的环。然而，Gorenstein环的类要普遍得多，而且众所周知(在Bass之后)无处不在。证明了当R是具有特征p的剩余域k的正则局部环时，Greenlees证明了THH(R；k)是Gorenstein的，并从两个方面推广了这一结果。首先，当R是Gorenstein(而不仅仅是正则的)时，人们认为这是真的，这将极大地丰富例子的范围。其次，当R具有反对合时，似乎更丰富的等变版本适用于实THH；这涉及将上述工作与Dotto和Patchkoria的工作相结合，并与Meier就Gorenstein对偶进行BPR。在这样做的过程中，将开发一些有趣的谱序列，这些序列将对显式计算有用。