Substitution maps in the Robba ring

On the Slope Filtration of d - modules over the Robba Ring

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated 6tale (o, F)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily etale (ý, F)-modules over the Robba ring, of the Euler-Poincard characteristic formula and Tate local duality for p-adic represe...

Cohomology and duality for (φ,Γ)-modules over the Robba ring

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated étale (φ,Γ)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily étale (φ,Γ)-modules over the Robba ring, of the Euler-Poincaré characteristic formula and Tate local duality for p-adic represent...

SMOOTHING RING MAPS Contents

SMOOTHING RING MAPS Contents

Our exposition follows Swan’s, but we first prove an intermediate result which let’s us work in a slightly simpler situation. Here is an overview. We first solve the following “lifting problem”: A flat infinitesimal deformation of a filtered colimit of smooth algebras is a filtered colimit of smooth algebras. This result essentially says that it suffices to prove the main theorem for maps betwe...

SMOOTHING RING MAPS Contents