Preprints

1. On derived D-modules and their several definitions: arXiv:2510.15665. Abs

The so called theory of derived D-modules is an extension of classical D-modules to derived algebraic geometry, which uses the derived information of the base scheme. We prove that the three different definitions of derived D-modules, given by Beraldo, Nuiten and Toën-Vezzosi, on a (nice) derived scheme yield equivalent symmetric monoidal ∞-categories. We deduce this as a corollary of more general statements about Chevalley-Eilenberg cohomology of dg-Lie algebroids, proving a conjecture by E. Pavia, and about the relation between representations of a dg-Lie algebroid and some class of ind-coherent sheaves on the associated formal moduli problem, which can be of independent interest.

Some Old Writings

Caveat lector

• Master’s thesis: Derived moduli spaces of G-bundles.
  Written in Orsay under the supervision of Benjamin Hennion.
• Bachelor’s thesis: Analytic functions on p-adic fields.
  Written in Padua under the supervision of Maurizio Cailotto.
• Notes on the vertex algebra structure on chiral differential operators on an algebraic group.
  Written in Orsay for the M2 advanced course Introduction to Vertex Algebras by Anne Moreau.
• Notes on Grothendieck topologies.
  Written for the Scuola Galileiana’s course Introduction to category theory by Riccardo Colpi.
• Notes on Spectral Sequences.
  Written for the Algant master course Topology 2 by Andrea D’Agnolo.