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By James D. Lewis

This publication offers an creation to a subject matter of important curiosity in transcendental algebraic geometry: the Hodge conjecture. which include 15 lectures plus addenda and appendices, the amount is predicated on a sequence of lectures added via Professor Lewis on the Centre de Recherches Mathematiques (CRM). The ebook is a self-contained presentation, thoroughly dedicated to the Hodge conjecture and comparable themes. It contains many examples, and such a lot effects are thoroughly confirmed or sketched. the inducement in the back of the various effects and historical past fabric is equipped. This entire method of the ebook supplies it a ``user-friendly'' sort. Readers needn't seek in different places for varied effects. The publication is appropriate to be used as a textual content for a subject matters path in algebraic geometry; comprises an appendix via B. Brent Gordon.

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2). 1. 4, et sous l'hypoth~se suppldmentaire, sans doute superf6tatoire (conjecture de Bloch sur les surfaces avec H 2(X, Ox) = 0), que l'application d'A1banese A0(X) ~ Al_~bx(k) est un isomorphisme, Saito [$2] d6montre qu'en fait t'accouplement Ao(X) x B r ( X ) ~ Q/Z est non d6g6n6r6 £ gauche. __qc~),Q / l ) . gc°),Q/Z). l Hom(Br(X),Q/i[) l-" Ainsi le noyau de la fl~che verticale de gauche est inclus dans le noyau de la fl~che horizontale sup6rieure, qui par l'hypoth~se suppl@mentaire est un groupe de torsion.

P. ) Kluwer Academic Publishers 1989. [R3] W. - - On g l of curves over global fields, Math. Ann. 288 (1990) 179-193. IS1] S. SAITO. F. P. ) Kluwer Academic Publishers 1989. [$2] S. - - A conjecture of Bloch and Brauer groups of surfaces over p-adic fields, preprint, May 1990. [$3] S. SAITO. --- Torsion zero-cycles and 6taie homology of singular schemes, Duke Math. J. 64 (1991) 71-83. [$4] S. SAITO. - - Cycle map on torsion algebraic cycles of codimension two, Invent. Math. 106 (1991) 443-460. [Sbl] P.

4] S. SAITO. - - Cycle map on torsion algebraic cycles of codimension two, Invent. Math. 106 (1991) 443-460. [Sbl] P. - - Zero-cycles on rational surfaces over number fields, Invent. Math. 91 (1988) 505-524. [Sb2] P. SALBERGER. - - Chow groups of codimension two and l-adic realizations of motivic cohomology, typescript, September 1991. [Sc] C. SoloEd. - - Some examples of torsion in the Griffiths group, Math. Ann. 293 (1992) 651-679. [ S o ] M. - On Milnor K-groups attached to semi-abelian varieties, Journal of K-theory 4 (1990) 105-119.

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