Algebraic Geometry Seminar
The BPS decomposition theorem
- Date : 2026/01/14 (Wed.)
- Location : Seminar Room 714, Institute of Mathematics (NTU Campus)
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Speaker : Lucien Hennecart (CNRS)
- Organizer : Ionut Ciocan-Fontanine and Adeel Khan and Y.P. Lee (AS)
- Abstract : In this talk, I will explain joint work with Tasuki Kinjo (Kyoto), whose goal is to establish a quantitative version of the decomposition theorem (in the sense of Beilinson-Bernstein-Deligne-Gabber) for the morphism from a symmetric algebraic stack to its good moduli space.
This result provides a formula allowing one to reconstruct the cohomology of smooth stacks from the intersection cohomology of the stacks of graded points. It has applications to the study of the Borel-Moore homology of 0-shifted symplectic stacks and to the critical cohomology of (-1)-shifted symplectic stacks. I will discuss consequences for the purity of Hodge structures and a Kirwan surjectivity theorem for the restriction morphism to the semistable locus.
