Finite-Dimensional Motives and the Conjectures of Beilinson and Murre |
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Authors: | V Guletskii and C Pedrini |
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Institution: | (1) Institute of Mathematics, Surganova 11, 220072 Minsk, Belarus;(2) Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy |
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Abstract: | We relate the notion of finite dimensionality of the Chow motive M(X) of a smooth projective variety X (as defined by S. Kimura) with the conjectures of Beilinson, Bloch and Murre on the existence of a filtration on the Chow ring CH*(X). We show (Theorem 3) that finite dimensionality of M(X) implies uniqueness, up to isomorphism, of Murre's decomposition of M(X). Conversely (Theorem 4), Murre's conjecture for X
m
×X
m
(for a suitable m) implies finite-dimensionality of M(X). We also show (Theorem 7) that, for a surface X with p
g
= 0, the motive M(X) is finite-dimensional if and only if the Chow group of 0-cycles of X is finite-dimensional in the sense of Mumford, i.e. iff the Bloch conjecture holds for X.The second named author is a member of GNSAGA of CNR. |
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Keywords: | algebraic cycles motives Chow– Kü nneth decomposition motivic finite-dimensionality algebraic surfaces balanced varieties |
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