D-modules in derived algebraic geometry

par Carlo Buccisano (Université Paris-Saclay)

mardi 25 mars 2025, 14:00 → 15:00 Europe/Paris

IMT 1R2 207 (Salle Pellos)

After brief recalls (of classical D-modules and derived algebraic geometry), we'll introduce different notions of D-modules in the setting of derived algebraic geometry.

One natural definition is sheaves on the de Rham space, but it ignores any derived structure on the base scheme. We'll then explain how "derived D-modules", meaning a version of D-modules that remembers and exploits derived information, can be defined. One can follow either Toën-Vezzosi (derived foliations) or Nuiten and Beraldo (dg Lie algebroids).

These two definitions are apparently different : the main theorem of the talk will be their equivalence, proved by constructing an (∞-)enhancement of the functor of (completed) Hodge-filtered Chevalley-Eilenberg cohomology of (dg) Lie algebroids.