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Seminar on A1-topology, motives and K-theory

J-invariant of orthogonal involutions

by Maksim Zhykhovich (LMU Munich)

Europe/Moscow
818-1526-4739 (Zoom)

818-1526-4739

Zoom

Description

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.