[en] The goal of this project has been to give a classification of the forms of Picard-Vessiot extensions defined over a differential field with field of constants $\mathbb{Q}_{p}$, which is not algebraically closed, and with differential Galois group $O\left(2, \mathbb{Q}_{p}\right)$ or $S O\left(2, \mathbb{Q}_{p}\right)$. To do so we present a theoretical background in algebraic geometry, group cohomology and differential Galois theory.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Teresa Crespo Vicente