Equivariant pretheory
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General Introduction
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arXiv:1007.3780 Equivariant pretheories and invariants of torsors from arXiv Front: math.AG by Stefan Gille, Kirill Zainoulline 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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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
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