The generalized Hodge conjecture for stably nondegenerate abelian varieties

Fumio Hazama

Compositio Mathematica (1994)

  • Volume: 93, Issue: 2, page 129-137
  • ISSN: 0010-437X

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Hazama, Fumio. "The generalized Hodge conjecture for stably nondegenerate abelian varieties." Compositio Mathematica 93.2 (1994): 129-137. <http://eudml.org/doc/90317>.

@article{Hazama1994,
author = {Hazama, Fumio},
journal = {Compositio Mathematica},
keywords = {generalized Hodge conjecture; stably nondegenerate abelian varieties; Young diagrams},
language = {eng},
number = {2},
pages = {129-137},
publisher = {Kluwer Academic Publishers},
title = {The generalized Hodge conjecture for stably nondegenerate abelian varieties},
url = {http://eudml.org/doc/90317},
volume = {93},
year = {1994},
}

TY - JOUR
AU - Hazama, Fumio
TI - The generalized Hodge conjecture for stably nondegenerate abelian varieties
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 93
IS - 2
SP - 129
EP - 137
LA - eng
KW - generalized Hodge conjecture; stably nondegenerate abelian varieties; Young diagrams
UR - http://eudml.org/doc/90317
ER -

References

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  1. 1 N. Bourbaki, Groupes et Algèbres de Lie, chaps. VII-VIII, Hermann, Paris, 1975. Zbl0329.17002MR453824
  2. 2 P. Deligne, "Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques," Automorphic forms, Representations and L-functions, Proc. Sympos. Pure Math. vol. 33, part 2, Amer. Math. Soc., Providence, R.I. 1979, pp. 247-289. Zbl0437.14012MR546620
  3. 3 P. Deligne, "Hodge cycles on abelian varieties," Hodge Cycles, Motives, and Shimura Varieties, Lect. Notes in Math. 900, Springer-Verlag, Berlin- Heidelberg, 1982, pp. 9-100. Zbl0537.14006
  4. 4 M. Fischler, Young-tableau methods for Kronecker products of representations of the classical groups, J. Math. Phys.22 (1981), 637-648. Zbl0463.22017MR617303
  5. 5 A. Grothendieck, Hodge's general conjecture is false for trivial reasons, Topology8 (1969), 299-303. Zbl0177.49002MR252404
  6. 6 F. Hazama, Algebraic cycles on certain abelian varieties and powers of special surfaces, J. Fac. Sci. Univ. Tokyo31 (1985), 487-520. Zbl0591.14006MR776690
  7. 7 F. Hazama, Algebraic cycles on nonsimple abelian varieties, Duke Math. J.58 (1989), 31-37. Zbl0697.14028MR1016412
  8. 8 D. Mumford, Abelian varieties, Tata Inst. and Oxford Univ. Press, 1970. Zbl0223.14022MR282985
  9. 9 A.L. Onishchik, E.B. Vinberg, Lie groups and algebraic groups, Springer-Verlag, Berlin-Heidelberg, 1990. Zbl0722.22004MR1064110
  10. 10 J.-P. Serre, Résumè des cours de 1984-85, Collège de France. 
  11. 11 T. Shioda, "What is known about the Hodge conjecture?" Algebraic varieties and analytic varieties, Advanced Studies in Pure Mathematics 1, Kinokuniya, Tokyo, 1983, pp. 55-68. Zbl0527.14010MR715646
  12. 12 J.H.M. Steenbrink, "Some remarks about the Hodge conjecture," Hodge Theory, Lect. Notes in Math. 1246, Springer-Verlag, Berlin- Heidelberg, 1987, pp. 165-175. Zbl0629.14004MR894051
  13. 13 Y.G. Zarkhin, Weights of simple Lie algebras in the cohomology of algebraic varieties, Math. USSR, Izv., 24 (1985), 245-281. Zbl0579.14019MR740792
  14. 14 Y.G. Zarkhin, "Linear irreducible Lie algebras and Hodge structures," Algebraic geometry, Lect. Notes in Math. 1479, Springer-Verlag, Berlin-Heidelberg, 1991, pp. 281-297. Zbl0764.17006MR1181219

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