The J-invariant over splitting fields of Tits algebras

Abstract

We describe the J-invariant of a semi-simple algebraic group G over a generic splitting field of a Tits algebra of G in terms of the J-invariant over a base field. As a consequence we prove a 10 years 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.