Equivariant pretheory

• 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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• Comments Posted

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• General Introduction
• Search results
• Online References
• Paper References
• Definition
• Properties
• Standard theorems
• Open Problems
• Connections to Number Theory
• Computations and Examples
• History and Applications
• Some Research Articles
• Other Information
• Comments Posted
• Comments