A generic characterization of direct summands for orthogonal involutions

Anne Quéguiner-Mathieu (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

The `transcendental methods' in the algebraic theory of quadratic forms are based on two major results, proved in the 60's by Cassels and Pfister, and known as the representation and the subform theorems. A generalization of the representation theorem was proven by Jean-Pierre Tignol in 1996, in the setting of central simple algebras with involution. This paper studies the subform question for orthogonal involutions. A generic characterization of direct summands is given; an analogue of the subform theorem is proven for division algebras and algebras of index at most $2$.

Mots clés: Algebras with involution; Quadratic forms; Subform theorem

Domaines: Anneaux et algèbres [math.RA]

Anne Quéguiner-Mathieu. A generic characterization of direct summands for orthogonal involutions. 2006. ⟨hal-00091207⟩