Some abelian threefolds with nontrivial Griffiths group

David S. Zelinsky

Compositio Mathematica (1991)

  • Volume: 78, Issue: 3, page 315-355
  • ISSN: 0010-437X

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Zelinsky, David S.. "Some abelian threefolds with nontrivial Griffiths group." Compositio Mathematica 78.3 (1991): 315-355. <http://eudml.org/doc/90094>.

@article{Zelinsky1991,
author = {Zelinsky, David S.},
journal = {Compositio Mathematica},
keywords = {infinite Griffiths groups; abelian threefolds},
language = {eng},
number = {3},
pages = {315-355},
publisher = {Kluwer Academic Publishers},
title = {Some abelian threefolds with nontrivial Griffiths group},
url = {http://eudml.org/doc/90094},
volume = {78},
year = {1991},
}

TY - JOUR
AU - Zelinsky, David S.
TI - Some abelian threefolds with nontrivial Griffiths group
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 78
IS - 3
SP - 315
EP - 355
LA - eng
KW - infinite Griffiths groups; abelian threefolds
UR - http://eudml.org/doc/90094
ER -

References

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  2. 2 A. Beilinson, Higher regulators and values of L-functions, J. Soviet Math.30 (1985), 2036-2070. Zbl0588.14013
  3. 3 S. Bloch, Algebraic cycles and values of L-functions, J. reine angew. Math.350 (1984), 94-107. Zbl0527.14008MR743535
  4. 4 S. Bloch, Algebraic cycles and values of L-functions. II. Duke Math. J.52 (1985), 379-397. Zbl0628.14006MR792179
  5. 5 G. Ceresa-Genet, C is not algebraically equivalent to C - in its Jacobian, Ann. of Math. (2) 117 no. 2 (1983), 285-291. Zbl0538.14024MR690847
  6. 6 H. Clemens, Homological equivalence, modulo algebraic equivalence, is not finitely generated, I.H.E.S. Publ. Math.58 (1983), 19-38. Zbl0529.14002MR720930
  7. 7 P. Deligne, Courbes elliptiques: formulaire, in Modular functions of one variable. IV, Lecture Notes in Math. Vol. 476, Springer-Verlag, New York (1975), pp. 53-74. Zbl1214.11075MR387292
  8. 8 P. Deligne, Resumés des Premiers exposés de A. Grothendieck, in Groupes de Monodromie en Géométrie Algébrique (SGA 7, I), Lecture Notes in Math. Vol. 288, Springer-Verlag, New York (1972), exposé 1. Zbl0267.14003
  9. 9 P. Deligne et al., Cohomologie Etale (SGA 4 1/2), Lecture Notes in Math. Vol. 569, Springer-Verlag, New York (1977). Zbl0345.00010MR463174
  10. 10 P.A. Griffiths, On the periods of certain rational integrals. II. Ann. of Math. (2) 90 (1969), 496-541. Zbl0215.08103MR260733
  11. 11 B. Harris, Harmonic volumes, Acta Math.150 (1983), 91-123. Zbl0527.30032MR697609
  12. 12 B. Harris, Homological versus algebraic equivalence in a Jacobian, Proc. Natl. Acad. Sci. USA80 (Feb. 1983), 1157-1158. Zbl0523.14006MR689846
  13. 13 J.S. Milne, Etale cohomology, Princeton University Press, Princeton, New Jersey (1980). Zbl0433.14012MR559531
  14. 14 W. Raskind, A finiteness theorem in the Galois cohomology of algebraic number fields, Trans. Amer. Math. Soc.303 (1987) no. 2, 743-749. Zbl0648.12009MR902795
  15. 15 C. Schoen, Complex multiplication cycles and a conjecture of Beilinson and Bloch, preprint. Zbl0811.14003MR1107030
  16. 16 J. Tate, W.C.-groups over p-adic fields, Séminaire Bourbaki, 1957-58, exposé 156. Zbl0091.33701
  17. 17 J. Top, Hecke L-series related with algebraic cycles or with Siegel modular forms, Doctoral thesis, University of Utrecht, The Netherlands, 1989. 

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