Correspondence homomorphisms for singular varieties
Friedlander, Eric M. ; Mazur, Barry
Annales de l'Institut Fourier, Tome 44 (1994), p. 703-727 / Harvested from Numdam

Nous étudions la notion de correspondance géométrique entre des variétés algébriques (éventuellement singulières) et nous obtenons des résultats de comparaison entre plusieurs filtrations naturelles de l’homologie des variétés.

We study certain kinds of geometric correspondences between (possibly singular) algebraic varieties and we obtain comparison results regarding natural filtrations on the homology of varieties.

@article{AIF_1994__44_3_703_0,
     author = {Friedlander, Eric M. and Mazur, Barry},
     title = {Correspondence homomorphisms for singular varieties},
     journal = {Annales de l'Institut Fourier},
     volume = {44},
     year = {1994},
     pages = {703-727},
     doi = {10.5802/aif.1415},
     mrnumber = {95j:14009},
     zbl = {0811.14007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1994__44_3_703_0}
}
Friedlander, Eric M.; Mazur, Barry. Correspondence homomorphisms for singular varieties. Annales de l'Institut Fourier, Tome 44 (1994) pp. 703-727. doi : 10.5802/aif.1415. http://gdmltest.u-ga.fr/item/AIF_1994__44_3_703_0/

[AF] A. Andreotti and T. Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math., (2) 69 (1959), 713-717. | MR 31 #1685 | Zbl 0115.38405

[B] D. Barlet, Notes on the “Joint Theorem”, preprint, Institut Elie Cartan, Université Nancy, 1991.

[D] A. Dold, Lectures on Algebraic Topology, Springer-Verlag, 1972. | MR 415602 | MR 54 #3685 | Zbl 0234.55001

[DT] A. Dold and R. Thom, Quasifaserungen und unendliche symmetrische produkte, Ann. of Math., (2) 67 (1958), 239-281. | MR 97062 | MR 20 #3542 | Zbl 0091.37102

[F1] E. Friedlander, Algebraic cycles, Chow varieties, and Lawson homology, Compositio Mathematica, 77 (1991), 55-93. | Numdam | MR 1091892 | MR 92a:14005 | Zbl 0754.14011

[F2] E. Friedlander, Filtrations on algebraic cycles and homology, to appear in Ann. Ec. Norm. Sup. | Numdam | MR 1326671 | Zbl 0854.14006

[FG] E. Friedlander and O. Gabber, Cycle spaces and intesection theory, in Topological Methods in Modern Mathematics, Publish or Perish 1993, 325-370. | MR 1215970 | MR 94j:14010 | Zbl 0830.14008

[FL] E. Friedlander and H. B. Lawson, A theory of algebraic cocycles, Annals of Math., 136 (1992), 361-428. | MR 1185123 | MR 93g:14013 | Zbl 0788.14014

[FM] E. Friedlander and B. Mazur, Filtrations on the homology of algebraic varieties, to appear as a Memoir of the A.M.S. | MR 1211371 | Zbl 0841.14019

[G] A. Grothendieck, Hodge's general conjecture is false for trivial reasons, Topology, 8 (1969), 299-303. | MR 40 #5624 | Zbl 0177.49002

[H] H. Hironaka, Triangulation of algebraic sets, pp. 165-185, in Algebraic Geometry, Arcata 1974 : Proceedings of a Symposium in Pure Mathematics 29, A.M.S. Providence, 1975. | MR 51 #10331 | Zbl 0332.14001

[L] H. B. Lawson, Algebraic cycles and homotopy theory, Annals of Math., 129 (1989), 253-291. | MR 90h:14008 | Zbl 0688.14006

[LM] H. B. Lawson and M. L. Michelsohn, Algebraic cycles, Bott periodicity, and the Chern characteristic map, The Mathematical Heritage of Herman Weyl, AMS 1988, 241-264. | MR 90d:14010 | Zbl 0665.14001

[LF] P. Lima-Filho, Completion and fibrations for topological monoids and excision for Lawson homology, Trans. A.M.S., 340, n° 1 (1993), 127-147. | MR 94a:55009 | Zbl 0788.55013

[MS] D. Mcduff and G. Segal, Homology fibrations and the “group completion” theorem, Inventiones Math., 31 (1967), 279-284. | MR 53 #6547 | Zbl 0306.55020

[M] J. Milnor, On spaces having the homotopy type of a CW complex, Trans. A.M.S., 90 (1959), 272-280. | MR 20 #6700 | Zbl 0084.39002

[MM] J. Milnor and J. Moore, On the structure of Hopf algebras, Annals of Math., (2) 81 (1965), 211-264. | MR 30 #4259 | Zbl 0163.28202

[V] V. Voevodsky, Harvard Ph. D Thesis, 1992.