The J-invariant, Tits algebras and Triality

Abstract

In the present paper we set up a connection between the indices of the Tits algebras of a simple linear algebraic group $G$ and the degree one parameters of its motivic $J$-invariant. Our main technical tool are the second Chern class map and Grothendieck's $\gamma$-filtration. As an application we recover some known results on the $J$-invariant of quadratic forms of small dimension; we describe all possible values of the $J$-invariant of an algebra with orthogonal involution up to degree 8 and give explicit examples; we establish several relations between the $J$-invariant of an algebra $A$ with orthogonal involution and the $J$-invariant of the corresponding quadratic form over the function field of the Severi-Brauer variety of $A$.

28pp

References in corpus (3)

• Hyperbolicity of orthogonal involutions
• Addendum to: Generically split projective homogeneous varieties
• Isotropy of orthogonal involutions

Cited by in corpus (4)

• Shells of twisted flag varieties and the Rost invariant
• Hopf-theoretic approach to motives of twisted flag varieties
• Triality over Schemes
• The J-invariant and Tits algebras for groups of inner type E6