The fundamental curve of p-adic Hodge theory
Vortrag von Prof. Dr. Laurent Fargues
Sprecher eingeladen von: Prof. Dr. Joseph Ayoub
Datum: 21.10.13 Zeit: 13.15 - 14.45 Raum: Y27H25
I will explain the construction of a "complete algebraic curve" over the p-adic numbers that allows us the reprove in a very natural way some of the main theorems of p-adic Hodge theory: weakly admissible implies admissible and the p-adic monodromy theorem. This curve looks like the projective line, it is in some sens of genus zero, but differs subtly from it and admits for example semi-stable vector bundles with non integral slope. Seen as a compact p-adic Riemann surface it is uniformized by an open punctured disk where the coordinate is the prime number p. One of the main results is a classification theorem for vector bundles that generalizes the one of Grothendieck for the Riemann sphere. This is joint work with J.-M. Fontaine.