The arithmetic theory of elliptic curves enters the new century with some of its major secrets intact. Most notably, the Birch and Swinnerton-Dyer conjecture, which relates the arithmetic of an elliptic curve to the analytic behaviour of its associated L-series, is still unproved in spite of important advances in the last decades, some of which are recalled in Chapter 1. In the 1960’s the pione...

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.

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...