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Mini-course: On the Hasse Principle for Divisibility in commutative algebraic groups

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Laura Paladino
University of Calabria/MPIM
Fri, 13/04/2018 - 10:15 - Fri, 27/04/2018 - 12:00
MPIM Lecture Hall

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.


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