The Hasse Priciple is a fundamental topic in number theory. Anyway a complete proof is very seldom showed in undergraduate and graduate courses in number theory. We will decribe this classical result and prove it. After an overview of some long-established local-global principles, we will focus on the recent local-global question for divisibility in commutative algebraic group. In particular we will explain its relation with the Hasse principle for divisibility of elements of the Tate-Shavarevich group in the Weil-Châtelet group. This latter problem arose as a generalization of a classical question considered by Cassels. We will describe the results achieved for the two problems during the last fifteen years and some questions that are still open.

© MPI f. Mathematik, Bonn | Impressum & Datenschutz |