I am a chargé de recherche of CNRS located at the Université Paris-Sud. See my
CV for details.
Grothendieck-Lefschetz for vector bundles, submitted. We extend the Grothendieck-Lefschetz theorem from SGA 2 about the triviality of line bundles on the punctured spectra of complete intersections to vector bundles.
Purity for the Brauer group, submitted. We complete the proof of a purity conjecture of Grothendieck: the cohomological Brauer group is insensitive to removing a closed subscheme of codimension ≥ 2 of a regular scheme.
The Ainf-cohomology in the semistable case (joint with Teruhisa Koshikawa), submitted. We extend the Ainf-cohomology of Bhatt–Morrow–Scholze to the case of semistable reduction and use it to analyze lattices in de Rham cohomology and reprove the Fontaine–Jannsen conjecture.