Speaker: Dr. Raoul Hallopeau (Sorbonne University)

Title: Toward a notion of holonomicity for coadmissible Dcap-modules

Time: 10:30-11:30  April 1, 2026 (Wednesday)

Place: MCM110

Abstract: Let X be a smooth, rigid analytic space. Ardakov-Wadsley have introduced a natural sheaf Dcap of rapidly converging differential operators over X, together with a category of coadmissible Dcap-modules that play the role of "coherent objects". Like the classical complex case, we would like to have a good category of holonomic objects in this context.

Bode has introduced a notion of holonomicity following a definition of Caro by forcing some of the cohomological operations, without proving that holonomic modules are "constructible" out of integrable connections. For my part, I have defined a characteristic variety for these modules in the one-dimensional case. In particular, a notion of "sub-holonomicity" for coadmissible Dcap-modules over a smooth, rigid curve follows. I will present this construction.