Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Tuesday, 22 November 2005, 16:00 - 17:00, lecture room 407 of the Mathematisch Instituut.

Adriano Marmora (Paris 13): Irregularity and Swan conductor of p-adic Galois representations

Abstract:

Fontaine defined a hierarchy on p-adic Galois representations : crystalline, semi-stable and de Rham. He also introduced numerical invariants that measure, for a potentially semi-stable representation, the defect for being semi-stable, namely the Swan and the Artin conductors of its Deligne module. Berger has associated with any de Rham representation a p-adic differential equation, that provided one way for proving the p-adic monodromy theorem : de Rham representations are potentially semi-stable (and vice versa). In this lecture, I will report on relation between Swan conductor of a de Rham representation and irregularity of its p-adic differential equation.

Reference: Adriano Marmora, ''Irrégularité et Conducteur de Swan p-adiques" (French) Documenta Math. Vol 9, No 20, (2004)