On phi-families

On families of phi , Gamma - modules

Berger and Colmez introduced a theory of families of overconvergent étale (φ,Γ)-modules associated to families of p-adic Galois representations over p-adic Banach algebras. However, in contrast with the classical theory of (φ,Γ)-modules, the functor they obtain is not an equivalence of categories. In this paper, we prove that when the base is an affinoid space, every family of (overconvergent) ...

On arithmetic families of filtered phi-modules and crystalline representations

We consider stacks of filtered φ-modules over rigid analytic spaces and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients over an open substack containing all classical points. Further we study a period morphism (defined by Pappas and Rapoport) from a stack parametrising integral data and de...

Inference in phi-families of distributions

phi-Amenable and phi-biflat Banach algebras

In this paper we study the concept of ph-biatness ofa Banach algebra A, where ph is a continuous homomorphism on A.We prove that if ph is a continuous epimorphism on A and A hasa bounded approximate identity and A is ph- biat, then A is ph-amenable. In the case where ph is an isomorphism on A we showthat the ph- amenability of A implies its ph-biatness.

A note on Phi-entropies and Phi-Sobolev inequalities