Equivariant pretheory

General Introduction
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Online References
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 Ktheory 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 Ktheory) spectral sequence for such a theory. As an application we generalize the theorem of KarpenkoMerkurjev on Gtorsors and rational cycles; to every Gtorsor E and a Gequivariant 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 Jinvariant 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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