p-Analytic and p-quasi-analytic vectors

Quasi-analytic Vectors and Quasi-analytic Functions

Analytic vectors in continuous p-adic representations

Given a compact p-adic Lie group G over a finite unramified extension L/Qp let GL/Qp be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible locally L-analytic GL/Qp -representations that coincides with passage to analytic vectors in case L = Qp. On the other hand, we study the functor ”passage to an...

Analytic P-adic Cell Decomposition and P-adic Integrals

Roughly speaking, the semialgebraic cell decomposition theorem for p-adic numbers describes piecewise the p-adic valuation of p-adic polyno-mials (and more generally of semialgebraic p-adic functions), the pieces being geometrically simple sets, called cells. In this paper we prove a similar cell decomposition theorem to describe piecewise the valuation of analytic functions (and more generally...

ANALYTIC p-ADIC CELL DECOMPOSITION AND INTEGRALS

We prove a conjecture of Denef on parameterized p-adic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic functions (and more generally of subanalytic functions), the pieces being geometrically simple sets, called cells. We also classify subanalytic sets up to subanalyt...

Hechler's Theorem for tall analytic P-ideals

We prove the following version of Hechler's classical theorem: For each partially ordered set (Q,≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal I (coded in the ground model) a co nal subset of (I,⊆∗) is order isomorphic to (Q,≤).