| Speaker: | Vladimir Sosnilo (RIKEN iTHEMS) |
|---|---|
| Title: | Negative K-theory of t-categories |
| Date (JST): | Thu, Nov 20, 2025, 13:30 - 15:00 |
| Place: | Seminar Room B |
| Abstract: |
To a small stable infinity-category C one associates a Z-indexed family of algebraic K-groups K_i(C). For a scheme X and C = Perf_X the negative K-groups contain information about singularities of X. In particular, they vanish if X is a regular scheme. More generally, Antieau, Geoner, and Heller showed that the negative K-groups of C vanish if C admits a bounded t-structure with a noetherian heart. They conjectured that it holds without the noetherian assumption and that, in general, the K-theory of C only depends on the heart of the t-structure, i.e. one has isomorphisms K_i(D^b(C^{heart})) = K_i(C) for all integers i. We disprove both parts of the conjecture using homotopy theoretic methods. This talk is based on joint work with Maxime Ramzi and Christoph Winges. |
