J-invariant of orthogonal involutions

by Maksim Zhykhovich (LMU Munich)

Wednesday 8 Dec 2021, 13:00 → 15:00 Europe/Moscow

818-1526-4739 (Zoom)

The $J$-invariant of a semi-simple algebraic group $G$ was introduced by Petrov, Semenov and Zainoulline in 2008. The $J$-invariant is a discrete invariant which encodes the motivic decomposition of the variety of Borel subgroups in $G$. Let $(A, \sigma)$ be a central simple algebra with orthogonal involution and trivial discriminant. The $J$-invariant of $(A,\sigma)$ is defined as $J(\mathrm{PGO}^+(A,\sigma))$. In this talk I will discuss how to reduce the computation of $J(A,\sigma)$ to the case of quadratic forms.

Video