Finitedimensional 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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Online References
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Paper References
Articles by Jannsen and by Kimura in the NagelPeters 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 finitedimensional, 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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