| Speaker: | Timothy Logvinenko (Cardiff University) |
|---|---|
| Title: | The Hochschild homology of a non-commutative symmetric quotient stack |
| Date (JST): | Thu, Apr 10, 2025, 13:30 - 15:00 |
| Place: | Seminar Room B |
| Abstract: |
Let $X$ be a smooth, quasi-projective complex variety with an action of a finite group $G$. In arXiv:math/0206256 Baranovsky gave a decomposition of the complex cohomology of the stack $[X/G]$ in terms of the cohomologies of the fixed point loci $X_g$ for $g \in G$. He constructed this decomposition for the Hochschild homology of $[X/G]$ which is isomorphic to the complex cohomology via the Hochschild-Kostant-Rosenberg isomorphism. It is natural to ask if a similar decomposition exists for non-commutative varieties. I will talk about the specific case where the permutation group $S_n$ acts on the $n$-th tensor power $V^{\otimes n}$ of a DG category V. |
