Crespo Vicente, TeresaCalderer i García, Genís2022-04-052022-04-052021-06-18https://hdl.handle.net/2445/184648Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Teresa Crespo Vicente[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.46 p.application/pdfengcc-by-nc-nd (c) Genís Calderer i García, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/es/Geometria algebraicaTreballs de fi de grauHomologiaTeoria de GaloisTeoria de grupsAlgebraic geometryBachelor's thesesHomologyGalois theoryGroup theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess