MATH Seminar

Title: Equivariant pretheories and invariants of torsors
Seminar: Algebra and Number Theory
Speaker: Kirill Zainoulline of University of Ottawa
Contact: Skip Garibaldi, skip@mathcs.emory.edu
Date: 2011-11-07 at 3:00PM
Venue: MSC E406
Download Flyer
Abstract: In this talk we introduce and study the notion of an equivariant pretheory. Basic examples of such pretheories are equivariant Chow groups, equivariant $K$-theory and equivariant algebraic cobordism. As a new example we define an equivariant version of the cycle (co)homology with coefficients in a Rost cycle module. We also provide a version of Merkurjev's spectral sequence for equivariant cycle homology. As an application we generalize the theorem of Karpenko-Merkurjev on $G$-torsors and rational cycles; to every $G$-torsor $E$ and a $G$-equivariant pretheory we associate a graded ring which serves as an invariant of $E$. In the case of Chow groups this ring encodes the information concerning the motivic $J$-invariant of $E$ and in the case of Grothendieck's $K_0$ it encodes the indexes of the respective Tits algebras.