ar X iv : m at h / 99 06 16 5 v 1 [ m at h . A G ] 2 4 Ju n 19 99 Albanese and Picard 1 - motives
نویسنده
چکیده
LetX be an n-dimensional algebraic variety over a field of characteristic zero. We describe algebraically defined Deligne 1-motives Alb(X), Alb−(X), Pic(X) and Pic−(X) which generalize the classical Albanese and Picard varieties of a smooth projective variety. We compute Hodge, l-adic and De Rham realizations proving Deligne’s conjecture for H, H2n−1, H 1 and H1. We investigate functoriality, universality, homotopical invariance and invariance under formation of projective bundles. We compare our cohomological and homological 1-motives for normal schemes. For proper schemes, we obtain an Abel-Jacobi map from the (LevineWeibel) Chow group of zero cycles to our cohomological Albanese 1-motive which is the universal regular homomorphism to semi-abelian varieties. By using this universal property we get “motivic” Gysin maps for projective local complete intersection morphisms.
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