Can we count sheaves when p = 0 ?
Organizers
Speaker
Jiaqi Fu
Time
Thursday, March 5, 2026 3:00 PM - 4:00 PM
Venue
A7-201
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Donaldson–Thomas theory (DT) provides a virtual count of coherent sheaves over complex Calabi–Yau 3-folds. From the deformation-theoretic perspective, DT invariants are the shadow of derived critical locus structures. One might be tempted to extend this picture to positive characteristic. However, the Cartier isomorphism makes the situation tricky, since there are too many cycles in de Rham cohomology in the mod p case. I will talk about the notion of infinitesimal shifted symplectic forms, suggested by Toën and Robalo, and a shifted Darboux theorem based on it. We hope this work can contribute to pursuing a DT theory in positive characteristic.