Hodge classes on self-products of a variety with an automorphism

Chad Schoen

Compositio Mathematica (1988)

  • Volume: 65, Issue: 1, page 3-32
  • ISSN: 0010-437X

How to cite

top

Schoen, Chad. "Hodge classes on self-products of a variety with an automorphism." Compositio Mathematica 65.1 (1988): 3-32. <http://eudml.org/doc/89882>.

@article{Schoen1988,
author = {Schoen, Chad},
journal = {Compositio Mathematica},
keywords = {Hodge conjecture; algebraic cycles; Weil Hodge structure on abelian 4- folds with complex multiplication},
language = {eng},
number = {1},
pages = {3-32},
publisher = {Kluwer Academic Publishers},
title = {Hodge classes on self-products of a variety with an automorphism},
url = {http://eudml.org/doc/89882},
volume = {65},
year = {1988},
}

TY - JOUR
AU - Schoen, Chad
TI - Hodge classes on self-products of a variety with an automorphism
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 65
IS - 1
SP - 3
EP - 32
LA - eng
KW - Hodge conjecture; algebraic cycles; Weil Hodge structure on abelian 4- folds with complex multiplication
UR - http://eudml.org/doc/89882
ER -

References

top
  1. [A] Aoki, N., On some arithmetic problems related to the Hodge cycles on the Fermat varieties, Math. Ann.266 (1983) 23-54. Zbl0506.14030MR722926
  2. [A-B] Atiyah, M.F. and Bott, R., A Lefschetz fixed point formula for elliptic differential operators, Bull. of the A.M.S. 72 (1966) 245-250. Zbl0151.31801MR190950
  3. [A-C-G-H] Arbarello, E. et al., Geometry of Algebraic Curves, Vol. 1, Grundlehren der math. Wissenschaften 267, Springer, New York (1985). Zbl0559.14017
  4. [B] Beauville, A., Variétés de Prym et Jacobiennes Intermédiares, Ann. Scient. Éc. Norm. Sup., 4e serie, t. 10 (1977) 309-391. Zbl0368.14018MR472843
  5. [B-S] Bloch, S. and Srinivas, V., Remarks on correspondences and algebraic cycles, Amer. J. of Math.105 (1983) 1235-1254. Zbl0525.14003MR714776
  6. [B-T] Bott, R. and Tu, L., Differential Forms in Algebraic Topology. Springer, New York (1982). Zbl0496.55001MR658304
  7. [C-M] Conte, A. and Murre, J.P., The Hodge conjecture for fourfolds admitting a covering by rational curves, Math. Ann.238 (1978) 79-88. Zbl0373.14006MR510310
  8. [D-M] Deligne, P., Hodge cycles on Abelian varieties, Notes by J.S. Milne, in " Hodge cycles, Motives, and Shimura varieties ", Lect. Notes in Math., 900, Springer (1982). Zbl0537.14006
  9. [F] Fulton, W., Rational equivalence on singular varieties, Publ. Math. I.H.E.S. 45 (1975) 147-167. Zbl0332.14002MR404257
  10. [G] Gross, B., On the periods of Abelian integrals and a formula of Chowla and Selberg, Invent. Math.45 (1978) 193-211. Zbl0418.14023MR480542
  11. [G-H] Griffiths, P. and Harris, J., Principles of Algebraic Geometry. John Wiley and Sons, New York (1978). Zbl0408.14001MR507725
  12. [Gi] Gilkey, P., Lefschetz fixed point formulas and the heat equation, in Partial differential equations and geometry, Proceedings of the Park City Conference, ed. C. Byrnes, Marcel Dekker Lecture Notes in Pure and Applied Mathematics48 (1979) 91-147. Zbl0405.58044MR535591
  13. [H] Hodge, W.V.D., The topological invariants of algebraic varieties, Proc. Int. Cong. Math.182-192 (1950). Zbl0048.41701MR46075
  14. [H-Z] Hirzebruch, F. and Zagier, D., The Atiyah-Singer Theorem and Elementary Number Theory. Publish or Perish, Boston (1974). Zbl0288.10001MR650832
  15. [K] Kleiman, S.L., Algebraic cycles and the Weil conjectures, in Dix Exposés sur la Cohomologie des Schémas, North-Holland, Amsterdam, 359-386 (1968). Zbl0198.25902MR292838
  16. [M] Murty, V.K., Exceptional Hodge classes on certain Abelian varieties, Math. Ann.268 (1984) 197-206. Zbl0521.14004MR744607
  17. [O] Oort, F., Finite group schemes, local moduli for Abelian varieties, and lifting problems, in Algebraic Geometry, Oslo1970 (F. Oort, ed.), Wolters-Noordhoff, 233-254 (1972). Zbl0239.14018
  18. [R] Ran, Z., Cycles on Fermat hypersurfaces, Compositio Math.42 (1980) 121-142. Zbl0463.14003MR594486
  19. [Ri] Ribet, K., Hodge classes on certain types of Abelian varieties, Am. J. Math.105 (1983) 523-538. Zbl0586.14003MR701568
  20. [S] Shioda, T., The Hodge conjecture for Fermat varieties, Math. Ann.245 (1979) 175-184. Zbl0403.14007MR552586
  21. [S2] Shioda, T., Algebraic Cycles on Abelian varieties of Fermat type, Math. Ann.258 (1981) 65-80. Zbl0515.14005MR641669
  22. [S3] Shioda, T., What is known about the Hodge conjecture?, in Advanced Studies in Pure Mathematics 1, Algebraic Varieties and Analytic Varities, 55-68 (1983). Zbl0527.14010MR715646
  23. [SGA6] Berthelot, P., Grothendieck, A., Illusie, L., et al., Théorie des Intersections et Théoreme de Riemann-Roch, SGA 6 1966/67, Springer Lecture Notes225 (1971). Zbl0218.14001MR354655
  24. [Sh] Shimura, G., On analytic families of polarized Abelian varieties and automorphic functions, Ann. of Math.78 (1963) 149-192. Zbl0142.05402MR156001
  25. [St] Steenbrink, J.H.M., Mixed Hodge structure on the vanishing cohomology, in Real and Complex Singularities, Oslo1976, P. Holm (ed.), Sijthoff and Noordhoff, 525-563 (1977). Zbl0373.14007MR485870
  26. [W] Weil, A., Abelian varieties and the Hodge ring, in Collected Papers III, (1979) 421-429. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.