El Teorema de Hasse-Minkowski

Abstract

[en] Hasse-Minkowski theorem states that a quadratic form has a non-trivial solution in $\mathbb{Q}$ if and only if there is a non-trivial solution in every completition. In this work we will study these completitions, their properties and their solutions in polynomials, the proof of the theorem and some applications and counterexamples in other polynomials than quadratic forms.