Contribution Exposé de recherche sur proposition
On the deformation theory of dg-categories
This is work in progress with Ludmil Katzarkov, Pranav Pandit and Bertrand Toën. I will explain how to use the theory of formal moduli problems of Lurie to obtain a better understanding of the deformation theory of a dg-category up to Morita equivalence, based on previous work by Preygel. This leads to a finiteness result about any formal deformation of a smooth and proper dg-category.