The J-invariant of algebras with orthogonal involution

Online seminar Quadratic forms, linear algebraic groups and beyond, Wednesdays 8:30-9:30am

https://uottawa-ca.zoom.us/j/99397061432?pwd=LzNBS1UrSVNJQ1ZiU28yWHAyNlV...

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 (in this talk we consider Chow motives). Let (A, \sigma) be a central simple algebra with orthogonal involution and trivial discriminant. The J-invariant of (A,\sigma) is defined as J(PGO^+(A,\sigma)). In this talk I will discuss a conjecture of Quéguiner Mathieu, Semenov and Zainoulline, which allows to reduce the computation of J(A,\sigma) to the case of quadratic forms.