Gorenstein duality for topological Hochschild homology and its real form.

最好的一类交换环是正则局部环（离多项式环不远），然后是从这些环中分解出一个正则序列得到的环。然而，Gorenstein环类更一般，并且（在Bass之后）普遍存在。事实证明，这也是真实的环同伦，和Greenlees表明，THH（R;k）是Gorenstein时，R是正规的局部环与剩余领域k的特征p.该项目是扩大这一结果在两个方向。首先，当R是Gorenstein（而不仅仅是正则的）时，人们期望它是真的，这将极大地丰富例子的范围。其次，它似乎是一个更丰富的同变版本适用于真实的THH时，R有一个反对合;这涉及到结合上述工作与工作的Dotto和Patchkoria，也工作Greenlees与迈耶Gorenstein对偶的BPR。在这样做的过程中，一些有趣的频谱序列将开发这将是有用的显式计算。

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.