# (attention à l'horaire !) Characteristic cycles for D^\dag-modules and the first Drinfeld covering

Vendredi, 14. décembre 2018 - 15:00 - 16:00
Orateur:

Konstantin Ardakov (Oxford)

Résumé:

Let $F$ be a finite extension of $\mathbb{Q}_p$. Using the theory equivariant $\mathcal{D}$-modules on rigid analytic spaces, it is possible to show that the global rigid-analytic functions on the first Drinfeld covering of the $p$-adic upper half-plane $P^1 - P^1(F)$ break up into a direct sum of finitely many irreducible coadmissible modules over the locally analytic distribution algebra of $GL_2(F)$. The proof uses techniques from the theory of arithmetic $\mathcal{D}^\dag$-modules, such as characteristic cycles and microlocalisation.