CRITICAL VARIETIES AND MOTIVIC EQUIVALENCE FOR ALGEBRAS WITH INVOLUTION - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Transactions of the American Mathematical Society Année : 2022

CRITICAL VARIETIES AND MOTIVIC EQUIVALENCE FOR ALGEBRAS WITH INVOLUTION

Résumé

Motivic equivalence for algebraic groups was recently introduced in [9], where a characterization of motivic equivalent groups in terms of higher Tits indexes is given. As a consequence, if the quadrics associated to two quadratic forms have the same Chow motives with coe cients in F 2 , this remains true for any two projective homogeneous varieties of the same type under the orthogonal groups of those two quadratic forms. Our main result extends this to all groups of classical type, and to some exceptional groups, introducing a notion of critical variety. On the way, we prove that motivic equivalence of the automorphism groups of two involutions can be checked after extending scalars to some index reduction field, which depends on the type of the involutions. In addition, we describe conditions on the base field which guarantee that motivic equivalent involutions actually are isomorphic, extending a result of Ho↵mann on quadratic forms.
Fichier principal
Vignette du fichier
2020-Equiv-Motivique.pdf (682.13 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03815191 , version 1 (14-10-2022)

Identifiants

Citer

Anne Quéguiner-Mathieu, Charles de Clercq, Maksim Zhykhovich. CRITICAL VARIETIES AND MOTIVIC EQUIVALENCE FOR ALGEBRAS WITH INVOLUTION. Transactions of the American Mathematical Society, 2022. ⟨hal-03815191⟩
37 Consultations
31 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More