We discuss some application of Jacquet modules in the study of parabolically induced representations of classical p-adic groups. The main problem that we consider is the construction of non-cuspidal square integrable representations. Since the problem is related to understanding of the reducibilityof the parabolically induced representations, we discuss also the reducibility questions.

Abstract In [16], Peterzil and Steinhorn proved that if a group G definable in an o -minimal structure is not definably compact, then contains torsion-free subgroup of dimension 1. We prove here p -adic analogue the Peterzil–Steinhorn theorem, special case abelian groups. Let be -adically closed field M . If compact there H 1 which compact. future paper we will generalize this to non-abelian

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...