Equivariant pretheories and invariants of torsors

Details Equivariant pretheories and invariants of torsors Equivariant pretheories and invariants of torsors

2010-07-22

arxiv.org/abs/1007.3780v2

Mathematics

Algebraic Geometry

23 pages; this is an essentially extended version of the previous preprint: the construction of an equivariant cycle (co)homol

Scientific paper

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an equivariant (co)homology theory with coefficients in a Rost cycle module and provide a version of Merkurjev's (equivariant K-theory) spectral sequence for such a theory. 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 -- indexes of the respective Tits algebras.

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