Algebraic equivalence of real algebraic cycles
Abánades, Miguel ; Kucharz, Wojciech
Annales de l'Institut Fourier, Tome 49 (1999), p. 1797-1804 / Harvested from Numdam
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Étant donné une variété algébrique réelle compacte non singulière, on étudie les classes de cohomologie algébrique données par les cycles algébriques, algébriquement équivalents à zéro.

Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.

@article{AIF_1999__49_6_1797_0,
     author = {Ab\'anades, Miguel and Kucharz, Wojciech},
     title = {Algebraic equivalence of real algebraic cycles},
     journal = {Annales de l'Institut Fourier},
     volume = {49},
     year = {1999},
     pages = {1797-1804},
     doi = {10.5802/aif.1738},
     mrnumber = {2001a:14061},
     zbl = {0932.14033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1999__49_6_1797_0}
}

Abánades, Miguel; Kucharz, Wojciech. Algebraic equivalence of real algebraic cycles. Annales de l'Institut Fourier, Tome 49 (1999) pp. 1797-1804. doi : 10.5802/aif.1738. http://gdmltest.u-ga.fr/item/AIF_1999__49_6_1797_0/

[1] S. Akbulut and H. King, Topology of Real Algebraic Sets, Mathematical Sciences Research Institute Publications, Springer, 1992. | MR 94m:57001 | Zbl 0808.14045

[2] S. Akbulut and H. King, Transcendental submanifolds of Rn, Comm. Math. Helv., 68 (1993), 308-318. | MR 94j:57032 | Zbl 0806.57017

[3] E. Bierstone and P. Milman, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. Math., 128 (1997), 207-302. | MR 98e:14010 | Zbl 0896.14006

[4] J. Bochnak and W. Kucharz, Algebraic models of smooth manifolds, Invent. Math., 97 (1989), 585-611. | MR 91b:14076 | Zbl 0687.14023

[5] A. Borel et A. Haefliger, La classe d'homologie fondamentale d'un espace analytique, Bull. Soc. Math. France, 89 (1961), 461-513. | Numdam | MR 26 #6990 | Zbl 0102.38502

[6] P.E. Conner, Differentiable Periodic Maps, Lecture Notes in Math., Vol. 738, Berlin-Heidelberg-New York, Springer, 1979. | MR 81f:57018 | Zbl 0417.57019

[7] W. Fulton, Intersection Theory, Ergebnisse der Math., Vol. 2, Berlin-Heidelberg-New York, Springer, 1984. | MR 85k:14004 | Zbl 0541.14005

[8] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math., 79 (1964), 109-326. | MR 33 #7333 | Zbl 0122.38603

[9] S.T. Hu, Homotopy Theory, New York, Academic Press, 1959. | MR 21 #5186 | Zbl 0088.38803

[10] W. Kucharz, Algebraic equivalence and homology classes of real algebraic cycles, Math. Nachr., 180 (1996), 135-140. | MR 97e:14009 | Zbl 0877.14003

[11] J. Milnor and J. Stasheff, Characteristic Classes, Ann. of Math. Studies, Vol. 76, Princeton Univ. Press, 1974. | MR 55 #13428 | Zbl 0298.57008

[12] R. Thom, Quelques propriétés globales de variétés différentiables, Comm. Math. Helv., 28 (1954), 17-86. | MR 15,890a | Zbl 0057.15502

[13] A. Tognoli, Su una congettura di Nash, Ann. Scuola Norm. Sup. Pisa, 27 (1973), 167-185.. | Numdam | MR 53 #434 | Zbl 0263.57011