2 results
The
$J$-invariant over splitting fields of Tits algebras
- Part of
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- 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
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- Article
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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.
Hopf-theoretic approach to motives of twisted flag varieties
- Part of
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- Journal:
- Compositio Mathematica / Volume 157 / Issue 5 / May 2021
- Published online by Cambridge University Press:
- 29 April 2021, pp. 963-996
- Print publication:
- May 2021
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Let
$G$ be a split semisimple algebraic group over a field and let 
$A^*$ be an oriented cohomology theory in the Levine–Morel sense. We provide a uniform approach to the 
$A^*$-motives of geometrically cellular smooth projective 
$G$-varieties based on the Hopf algebra structure of 
$A^*(G)$. Using this approach, we provide various applications to the structure of motives of twisted flag varieties.
