6533b7dbfe1ef96bd1270a6f
RESEARCH PRODUCT
The J-invariant, Tits algebras and Triality
Kirill ZainoullineAnne Quéguiner-mathieuNikita Semenovsubject
Linear algebraic groupDiscrete mathematicsInvolution (mathematics)Pure mathematicsAlgebra and Number TheoryChern classTrialityj-invariant010102 general mathematicsMathematics - Rings and Algebras01 natural sciencesMathematics - Algebraic GeometryRings and Algebras (math.RA)0103 physical sciencesFOS: Mathematics010307 mathematical physics0101 mathematicsAlgebraic Geometry (math.AG)Function field20G15 14C25 14L30 16W10 11E04Mathematicsdescription
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 $A$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-12-01 |