Algebraic cycles on generic abelian varieties

Najmuddin Fakhruddin

Compositio Mathematica (1996)

  • Volume: 100, Issue: 1, page 101-119
  • ISSN: 0010-437X

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Fakhruddin, Najmuddin. "Algebraic cycles on generic abelian varieties." Compositio Mathematica 100.1 (1996): 101-119. <http://eudml.org/doc/90419>.

@article{Fakhruddin1996,
author = {Fakhruddin, Najmuddin},
journal = {Compositio Mathematica},
keywords = {abelian variety; cycles generated by divisors; Chow groups; Griffiths group},
language = {eng},
number = {1},
pages = {101-119},
publisher = {Kluwer Academic Publishers},
title = {Algebraic cycles on generic abelian varieties},
url = {http://eudml.org/doc/90419},
volume = {100},
year = {1996},
}

TY - JOUR
AU - Fakhruddin, Najmuddin
TI - Algebraic cycles on generic abelian varieties
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 100
IS - 1
SP - 101
EP - 119
LA - eng
KW - abelian variety; cycles generated by divisors; Chow groups; Griffiths group
UR - http://eudml.org/doc/90419
ER -

References

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  3. 3 Borel, A.: Stable real cohomology of arithmetic groups. Manifolds and Lie groups, Progr. Math.14. Birkhauser, 1981. Zbl0483.57026MR642850
  4. 4 Bosch, A., Lutkebohmert, W. and Raynaud, M.: Neron Models. Springer Verlag, 1990. Zbl0705.14001MR1045822
  5. 5 Ceresa, G.: C is not algebraically equivalent to C- in its Jacobian. Ann.-of Math, 117:285-291, 1983. Zbl0538.14024MR690847
  6. 6 Colombo, E. and van Geemen, B.: Note on curves in a Jacobian. Compo.-Math, 88:333-353, 1993. Zbl0802.14002MR1241954
  7. 7 Deligne, P.: Theoreme de Lefschetz et Criteres de Degenerescence de Suites Spectrales. Inst.-Hautes-Etudes-Sci.-Publ.-Math, 35:19-68, 1968. Zbl0159.22501MR244265
  8. 8 Deligne, P.: La conjecture de Weil I. Inst.-Hautes-Etudes-Sci.-Publ.-Math, 43:273-307, 1974. Zbl0287.14001MR340258
  9. 9 Deninger, C. and Murre, J.: Motivic decomposition of abelian schemes and the Fourier transform. J.-Reine-Angew. -Math, 422:201-219,1991. Zbl0745.14003MR1133323
  10. 10 Dold, A.: Lectures on Algebraic Topology. Springer Verlag, 1972. Zbl0234.55001MR415602
  11. 11 Donagi, R. and Smith, R.: The Structure of the Prym map. Acta.-Math, 146:25-102,1981. Zbl0538.14019MR594627
  12. 12 Fakhruddin, N.: Algebraic cycles on generic Abelian varieties. PhD thesis, The University of Chicago, 1995. 
  13. 13 Faltings, G. and Chai, C-L.: Degeneration of Abelian Varieties. Springer Verlag, 1990. Zbl0744.14031MR1083353
  14. 14 Fulton, W.: Intersection Theory. Springer Verlag, 1984. Zbl0541.14005MR732620
  15. 15 Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann.-of-Math, 74:329-387, 1961. Zbl0134.03501MR142696
  16. 16 Mostafa, S.: Die Singularitaten der Modulmannigfaltigkeiten... J.-reine-Angew.-Math, 343:81-98, 1983. Zbl0526.14012MR705878
  17. 17 Nori, M.: Cycles on the generic Abelian threefold. Proc.-Ind.-Acad.-Sci, 99:191-196, 1989. Zbl0725.14006MR1032704
  18. 18 Nori, M.: Algebraic cycles and Hodge theoretic connectivity. Invent.-Math, 111:349-373, 1993. Zbl0822.14008MR1198814
  19. 19 Popp, H.: Moduli Theory and Classification Theory of Algebraic Varieties. LNM620. Springer Verlag, 1977. Zbl0359.14005MR466143
  20. 20 Saito, M.: Mixed Hodge modules. Publ.-Res.-Inst.-Math.-Sci.(Kyoto University), 26:221-333, 1990. Zbl0727.14004MR1047415
  21. 21 Zucker, S.: Locally homogeneous variations of Hodge structure. Enseign.-Math, 27:243-276, 1981. Zbl0584.14003MR659151

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