Сategorical quantizations of symplectic varieties in char p

par Dr Dmitry Kubrak (CNRS, Université Paris-Saclay)

vendredi 13 mars 2026, 15:00 → 16:30 Europe/Paris

salle Olga Ladyjenskaïa (ground floor) (IHP)

Originally motivated by physics, mathematically a quantization of a Poisson variety $X$ is simply a formal 1-parameter deformation of its sheaf of functions that in the first approximation agrees with the Poisson bracket. In the algebraic context such quantizations tend not to exist globally due to a possible non-vanishing of cohomology of relevant coherent sheaves. It was observed by Kontsevich that in the algebraic context it might in fact be more natural to consider formal deformations of the category $QCoh(X)$ rather than the sheaf of algebras $O_X$. I will talk about joint work with Bogdanova, Travkin and Vologodsky where, building on the work of Bezrukavnikov and Kaledin, we construct a canonical such categorical quantization for (restricted) symplectic varieties in char p. An interesting feature of char p is that this quantization in fact naturally extends from the formal disk to a family of categories over $\mathbb{P}^1$ which carries strong resemblance with the Simpson’s twistor space picture. This allows to associate to any restricted symplectic scheme a category of "mod p F-gauges", which agrees with Bhatt-Lurie F-gauges for Y in the case $X=T^*Y$. If time permits I will also talk about some further results about quantizations over $\mathbb{Z}/p^n$ or even $\mathbb{Z}$ (work in progress).