1 results
The
$J$-invariant over splitting fields of Tits algebras
- Part of
-
- Journal:
- Compositio Mathematica / Volume 160 / Issue 9 / September 2024
- Published online by Cambridge University Press:
- 11 September 2024, pp. 2100-2114
- Print publication:
- September 2024
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
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 
$\mathrm {D}_n$. In the case of type 
$\mathrm {D}_n$ we also provide explicit formulas for the first component and in some cases for the second component of the 
$J$-invariant.
