Generalization of Abel's theorem and some finiteness property of zero-cycles on surfaces

Hiroshi Saito

Compositio Mathematica (1992)

  • Volume: 84, Issue: 3, page 289-332
  • ISSN: 0010-437X

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Saito, Hiroshi. "Generalization of Abel's theorem and some finiteness property of zero-cycles on surfaces." Compositio Mathematica 84.3 (1992): 289-332. <http://eudml.org/doc/90186>.

@article{Saito1992,
author = {Saito, Hiroshi},
journal = {Compositio Mathematica},
keywords = {polarized Hodge structures of weight 2; vanishing of cycles in the intermediate jacobian; filtration on the Chow group},
language = {eng},
number = {3},
pages = {289-332},
publisher = {Kluwer Academic Publishers},
title = {Generalization of Abel's theorem and some finiteness property of zero-cycles on surfaces},
url = {http://eudml.org/doc/90186},
volume = {84},
year = {1992},
}

TY - JOUR
AU - Saito, Hiroshi
TI - Generalization of Abel's theorem and some finiteness property of zero-cycles on surfaces
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 84
IS - 3
SP - 289
EP - 332
LA - eng
KW - polarized Hodge structures of weight 2; vanishing of cycles in the intermediate jacobian; filtration on the Chow group
UR - http://eudml.org/doc/90186
ER -

References

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  1. 1 Angeniol, B.: Familles de cycles algébriques - schémas de Chow, Lecture Notes in Math.896, Springer Verlag, Berlin, Heidelberg, New York, 1981. Zbl0496.14004MR646062
  2. 2 Angeniol, B., and El Zein, F.: La classe fondamentale relative d'un cycle, Bull. Soc. Math. France, Memoire, 58 (1978), 67-93. Zbl0388.14003
  3. 3 Artin, M., Grothendieck, A., Verdier, J.-P.: Théorie des Topos et Cohomologie étales de schémas, exposé XVIII par Deligne, P., Lecture Notes in Math., 305, Springer Verlag, Berlin, Heidelberg, New York, 1973. Zbl0245.00002MR354654
  4. 4 Bloch, S.: Torsion algebraic cycles and a theorem of Roitman, Comp. Math., 39 (1979), 107-127. Zbl0463.14002MR539002
  5. 5 Bloch, S.: Lectures on algebraic cycles, Duke University Mathematics Series IV, Durham, 1980. Zbl0436.14003MR558224
  6. 6 Deligne, P.: Theorie de Hodge III, Publ. math. IHES, 44 (1974) 5-77. Zbl0237.14003MR498552
  7. 7 Kleiman, S.: Algebraic cycles and the Weil conjecture, in Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968. Zbl0198.25902MR292838
  8. 8 Merkur'ev, A.S., and Suslin, A.A.: K-cohomology of Brauer-Severi varieties and the norm residue homomorphism, Izv. Acad. Nauk, 46 (1982), 1011-1046(= Math. USSR. Izv.21 (1983), 307-340.) Zbl0525.18008MR675529
  9. 9 Roitman, A.A.: The torsion of the group of 0-cycles modulo rational equivalence, Ann. of Math., 111 (1980), 553-569. Zbl0504.14006MR577137
  10. 10 Saavedra, N.: Catégories Tannakiens, Lecture Notes in Math.265, Springer Verlag, Berlin, Heidelberg, New York, 1972. Zbl0241.14008MR338002
  11. 11 Saito, H.: The Hodge cohomology and cubic equivalences, Nagoya Math. J., 94 (1984) 1-41. Zbl0574.14005MR748090
  12. 12 Saito, H.: A note on cubic equivalences, Nagoya Math. J., 101 (1986) 1-26. Zbl0594.14008MR828914
  13. 13 Samuel, P.: Relations d'équivalence en géométrie algébrique, in Proceeding of International Congress of Mathematicians, 1958, Cambridge University Press, Cambridge, 1960. Zbl0119.36901MR116010
  14. 14 Severi, F.: Ulterior sviluppi della teoria delle serie di equivalenza sulle suerfidie algebriche, appendice I a Geometria dei sistemi algebrici sopra una superficie e sopra una varietà algebrica, vol. terzo, Edizioni Cremonese, Roma, 1959. MR104656
  15. 15 Verdier, J.-P.: Classes d'homologie associée à un cycle, Astérisque, 36-37 (1976), 101-151 (exposé VI). Zbl0346.14005
  16. 16 Weil, A.: Oeuvres Scientifiques, Collected papers, Vol. II, Corrected second printing, Springer Verlag, New York, Heidelberg, Berlin, 1980. Zbl0428.01012

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