Morava K(2)-motives and the Rost invariant

• 主讲人：Viktor Petrov (St. Petersburg State University)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2023-04-13 21:00 - 2023-04-13 22:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/D13210BBC42F4A64DA49AA34E4227E7E
Valid Until: 2027-05-31 23:59

 

Abstract: A principal homogeneous bundle under the action of a simple algebraic group determines invariants in the Brauer group called Tits algebras. In the case when the group is simply connected these invariants are trivial, but one can define a higher degree invariant called the Rost invariant. It follows from a result by I. Panin that the motives of full flag varieties with coefficients in the Grothendieck group K0 are isomorphic if and only if the Tits algebras generate the same subgroups in the Brauer group. We propose an analog of this result for the case of the Rost invariant; one considers Morava K-theory K(2) instead of K0.

 

Bio: Viktor Petrov is an associate professor at St. Petersburg State University. He got his PhD degree in 2005 and Dr.Sci. degree in 2022, both from St. Petersburg State University. He was a postdoc at the University of Alberta (Edmonton, AB) and Max Planck Institute (Bonn, Germany). Viktor Petrov was awarded by the St. Petersburg Mathematical Society the prize for young mathematicians and won the "Young Russian Mathematics" contest (twice).