The $J$-invariant over splitting fields of Tits algebras

Zhykhovich, Maksim (2024): The $J$-invariant over splitting fields of Tits algebras. In: Compositio Mathematica, Bd. 160, Nr. 9: S. 2100-2114

Abstract

We describe the J-invariant of a semisimple algebraic group G over a generic splitting field of a Tits algebra of G in terms of the J-invariant over the base field. As a consequence we prove a 10-year-old conjecture of Quéguiner-Mathieu, Semenov, and Zainoulline on the J-invariant of groups of type Dn. In the case of type Dn we also provide explicit formulas for the first component and in some cases for the second component of the J-invariant.

• Dokumententyp: Zeitschriftenartikel
• Keywords: linear algebraic groups; Tits algebras; algebras with involution; twisted flag varieties; Chow motives
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0010-437X
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 432236229