Gorenstein duality for topological Hochschild homology and its real form.

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.