Some model theory and topological dynamics of $p$-adic algebraic groups

Mackey Theory for p-adic Lie groups

This paper gives a p-adic analogue of the Mackey theory, which relates representations of a group of type G = H×tA to systems of imprimitivity.

PICARD GROUPS IN p-ADIC FOURIER THEORY

Let L 6= Qp be a proper finite field extension of Qp and o ⊂ L its ring of integers viewed as an abelian locally L-analytic group. Let ô be the rigid L-analytic group parametrizing the locally analytic characters of o constructed by Schneider-Teitelbaum. Let K/L be a finite extension field. We show that the base change ôK has a Picard group Pic(ôK) which is profinite and that the unit section i...

Comparison of some quotients of fundamental groups of algebraic curves over p-adic fields

THE MOD p REPRESENTATION THEORY OF p-ADIC GROUPS

1.1. The p-adic numbers. A rational number x ∈ Q× may be uniquely written as x = ab p n with a, b and n nonzero integers such that p ab. We define ordp(x) = n, |x|p = p−n, |0|p = 0. |·|p defines an absolute value on Q, satisfying the stronger ultrametric triangle equality |x+ y|p ≤ max(|x|p, |y|p). We define Qp to be the completion Q with respect to this metric and we use the same notation | · ...

THE MOD p REPRESENTATION THEORY OF p - ADIC GROUPS

Exercise 1 (Maximal compact subgroups of G). A lattice in Qp is a finitelygenerated Zp-submodule of Qp that generates Qp as vector space. In particular, it’s free of rank n. Note that G acts transitively on the set of lattices in Qp . (i) Show that K = StabG(Zp ). (ii) Suppose that K ′ is a compact subgroup of G. Show that K ′ stabilises a lattice. (Hint: show that the K ′-orbit of Zp is finite...