Invariants de Witt des involutions de bas degré en caractéristique 2

Abstract

A $3$-fold and a $5$-fold quadratic Pfister forms are canonically associated to every symplectic involution on a central simple algebra of degree $8$ over a field of characteristic $2$. The same construction on central simple algebras of degree $4$ associates to every unitary involution a $2$-fold and a $4$-fold Pfister quadratic forms, and to every orthogonal involution a $1$-fold and a $3$-fold quasi-Pfister forms. These forms hold structural information on the algebra with involution.

Keywords

• Algèbre simple centrale à involution
• composition de formes quadratiques
• formes quadratiques de Pfister