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Zbl 0686.14006
Suwa, Noriyuki
Sur l'image de l'application d'Abel-Jacobi de Bloch. (On the image of Bloch's Abel-Jacobi map). (French)
[J] Bull. Soc. Math. Fr. 116, No.1, 69-101 (1988). ISSN 0037-9484

The article studies Bloch's Abel-Jacobi homomorphism for a smooth projective scheme over an arbitrary field. The main result shows that the image of this mapping is generated by a finite set of correspondences and is used to give criteria for Bloch's homomorphism not to be surjective - for crystalline cohomology these are in terms of the slopes of cohomology. The last three sections show: the image is determined by the colevel filtration when resolution of singularities holds; for certain complete intersections Bloch's homomorphism vanishes; the slopes of a Dieudonné module for Murre's abelian variety of a scheme X are contained in those of $H\sp 3(X)$.
[G.Horrocks]

MSC 2000:: *14C35 Appl. of methods of algebraic K-theory
14C05 Parametrization

Keywords: Bloch's Abel-Jacobi homomorphism; slopes of cohomology; Dieudonné module

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