Finite-dimensional motives

• General Introduction

  Notion introduced by Kimura, see also O'Sullivan. A weaker condition is that of Schur finiteness; see Ayoub: The motivic vanishing cycle and the conservation conjecture (in Nagel and Peters, eds).

  See Pure motives

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• Search results

  MathSciNet

  Google Scholar

  Google

  arXiv: Experimental full text search

  arXiv: Abstract search

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• Online References

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• Paper References

  Articles by Jannsen and by Kimura in the Nagel-Peters volume II (Algebraic cycles and motives)

  Chapter 12 of André.

  Bourbaki seminar by André

  Andre: Motifs de dimension finie, S´eminaire Bourbaki.Vol. 2003/2004. Ast´erisque No. 299 (2005), Exp.No. 929, viii, 115–145. Very good, and long review in MR

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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

  Kimura: Chow motives can be finite-dimensional, in some sense.

  Guletskii article(s).

  Mazza and Del Padrone on Schur finiteness. Looks very good.

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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