Monodromy theorem

We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule of [V2]. As applications, we show that all Schubert problems for all Grassmannians are enumerative over the real numbers, and sufficiently large finite fields. We prove a generic smoothness theorem as a substitute for the Kleiman-Bertini theorem in positive characteristic.

25p noel_noel 17-01-2013 50 5   Download

We produce a canonical filtration for locally free sheaves on an open p-adic annulus equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on p-adic differential equations, analogous to Grothendieck’s local monodromy theorem (also a consequence of results of Andr´ and of Mebkhout). Namely, given a finite locally free sheaf on an open e p-adic annulus with a connection and a compatible Frobenius structure, the module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix. ...

93p tuanloccuoi 04-01-2013 44 6   Download