Raoul Hallopeau

Researh activity

Research team: number theory.

I work on arithmetic D-modules over a rigid analytic space.

Holonomic D-modules generalize the theory of connection modules and differential equations over a smooth variety. This theory is already well studied for algebraic varieties over a finite field in the work of Berthelot on arithmetic D-modules and of various other authors (Abe, Caro, Tsuzuki et al.). One of the main issues is to define a category of holonomic D-modules, stable by the six standard cohomological operations and generated by connection modules.

My thesis topic is to introduce a characteristic variety of coadmissible D-modules over a rigid analytic space. I am trying to define a good category of arithmetic holonomic modules stable by the six standard cohomological operations. I actually obtained such a notion in the dimension one case.

Publications and prepublications

• Raoul Hallopeau, Characteristic cycles for coadmissible D-modules on smooth rigid analytic curves, 2025

• Raoul Hallopeau, Cycle caractéristique pour les D-modules coadmissibles sur une courbe formelle, 2025

• Raoul Hallopeau, Microlocalisation d'opérateurs différentiels arithmétiques sur une schéma formel lisse , 2024

• Raoul Hallopeau, Dk-modules holonomes sur une courbe formelle , 2024

About me !

When I am not doing math, I like reading books. French literature, science fiction, children's books, fairy tales, I devour it all ! Otherwise, I practise some sport like swimming pool, hiking, table tennis ... And the rest of the time, I chat with my friends, chatty as I am !