Séminaire d'algèbre et de géométrie du 16-11-2023

Exposé de Fatma Kader Bingöl

Le 16-11-2023 à 15:45, en P108 et en ligne.

On the symbol length in positive characteristic

Résumé

We show that any central simple algebra of exponent p in prime characteristic p that is split by a p-extension of degree p^n is Brauer equivalent to a tensor product of 2.p^{n-1}-1 cyclic algebras of degree p. If p=2 and n ≥ 3, we improve this result by showing that such an algebra is Brauer equivalent to a tensor product of 5.2^{n-3}-1 quaternion algebras. Furthermore, we provide new proofs for some bounds on the symbol length of exponent-p algebras in prime characteristic p which have previously been obtained by different methods.