Etudiant : OUBANA FATIMA-ZAHRAE

Filière : Master Mathématiques Pures (MMP)

Encadrant : Pr. MONIRH KARIM

Annèe : 2025

Résumé : This thesis is divided into two main chapters. The first chapter introduces the theory of value functions on vector spaces and algebras. We present some facts on graded hermitian forms, which, as claimed above, allow to give a generalized version of Springer’s theorem on the Witt group. Furthermore, we present facts on some special value functions on simple algebras which are used in the study of anisotropic involutions. The second chapter of this work turns, in some abridged way, to the geometric and cohomological classification of central simple algebras. We briefly study the Brauer group through the lens of Galois cohomology and present how Severi–Brauer varieties encode essential algebraic information about central simple algebras. We end this chapter by giving Amitsur’s theorem, to show how these varieties can be applied in the study of Brauer group.