| Titre : | Filtrations on the homology of algebraic varieties | | Type de document : | texte imprimé | | Auteurs : | Eric M. FRIEDLANDER, Auteur ; Barry MAZUR, Auteur | | Editeur : | Providence, R. I. [Etats Unis] : American Mathematical Society | | Année de publication : | Cop. 1994 | | Collection : | Memoirs of the American Mathematical Society, ISSN 0065-9266 num. 529 | | Importance : | IX-110 p. | | ISBN/ISSN/EAN : | 978-0-8218-2591-4 | | Langues : | Anglais | | Catégories : | 14E20
20G20
46E25
54C40
| | Mots-clés : | cycle algébrique filtre homologie | | Résumé : | This work provides a detailed exposition of a classical topic from a very recent viewpoint. Friedlander and Mazur describe some foundational aspects of "Lawson homology" for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles. Attention is paid to methods of group completing abelian topological monoids. The authors study properties of Chow varieties, especially in connection with algebraic correspondences relating algebraic varieties. Operations on Lawson homology are introduced and analyzed. These operations lead to a filtration on the singular homology of algebraic varieties, which is identified in terms of correspondences and related to classical filtrations of Hodge and Grothendieck. | | Note de contenu : | bibliogr. |
Filtrations on the homology of algebraic varieties [texte imprimé] / Eric M. FRIEDLANDER, Auteur ; Barry MAZUR, Auteur . - Providence, R. I. (Etats Unis) : American Mathematical Society, Cop. 1994 . - IX-110 p.. - ( Memoirs of the American Mathematical Society, ISSN 0065-9266; 529) . ISBN : 978-0-8218-2591-4 Langues : Anglais | Catégories : | 14E20
20G20
46E25
54C40
| | Mots-clés : | cycle algébrique filtre homologie | | Résumé : | This work provides a detailed exposition of a classical topic from a very recent viewpoint. Friedlander and Mazur describe some foundational aspects of "Lawson homology" for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles. Attention is paid to methods of group completing abelian topological monoids. The authors study properties of Chow varieties, especially in connection with algebraic correspondences relating algebraic varieties. Operations on Lawson homology are introduced and analyzed. These operations lead to a filtration on the singular homology of algebraic varieties, which is identified in terms of correspondences and related to classical filtrations of Hodge and Grothendieck. | | Note de contenu : | bibliogr. |
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