Sobre el principi local-global en teoria de nombres

Abstract

[en] The aim of this Bachelor’s Thesis is to make an introduction of the local-global concept in Number Theory. In order to do this we construct the p-adic numbers in two different ways, we give some fundamental properties and we exhibit its structure. We present the Hilbert symbol in order to use it on the study of quadratic spaces and to determine which of them are isotropic and under which conditions. We use all the theory developed about quadratic spaces to finally formulate the Hasse-Minkowski theorem and we give a proof. In the last chapter, we show some counter-exemples of the Hasse principle, some of them classics and some others recently publicated.