Skip to main content
Log in

Addendum to: Hodge Classes on Self-Products of a Variety with an Automorphism

  • Published:
Compositio Mathematica

Abstract

There are infinitely many fundamentally distinct families of polarized Abelian fourfolds of Weil type with multiplication from the cyclotomic field of cube roots of unity. The Hodge conjecture is shown to hold at a sufficiently general fiber in any of these families.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • [Ba-Bo] Baily, W. and Borel, A.: Compactification of arithmetic quotients of bounded symmetric domains, Ann. Math.75 (1962) 342-381.

    Google Scholar 

  • [Bo] Borel, A.: Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem, J. Diff. Geom.6 (1972) 543-560.

    Google Scholar 

  • [Chai] Chai, C.-L.: Siegel Moduli Schemes and Their Compactifications over ℂ, in Arithmetic Geometry, G. Cornell and J. Silverman, editors, Springer-Verlag, New York (1986) 231-251.

    Google Scholar 

  • [C-W] Chevalley, C. and Weil, A.: Über das Verhalten der Integrale erster Gattung bei Automorphismen des Funktionenkörpers, Hamb. Abh.10 (1934) 358-361. Also in Weil, A.: Oeuvres Scientifiques, Springer-Verlag, New York, 1 (1979) 68-71.

    Google Scholar 

  • [De] Deligne, P., Variétés de Shimura: Interprétation modulaire, et techniques de construction de modèles canoniques, in Automorphic Forms, Representations, and L-functions, Proc. of Symposia in Pure Math.33 (2) (1979) 247-290.

    Google Scholar 

  • [D-M] Deligne, P. (Notes by Milne, J.): Hodge cycles on Abelian varieties, in Hodge Cycles, Motives and Shimura Varieties, Lect. Notes in Math.,SpringerVerlag, New York, 900 (1982) 9-100.

    Google Scholar 

  • [F] Faber, C.: Prym varieties of triple cyclic covers, Math. Z.199 (1988) 61-79.

    Google Scholar 

  • [H-N] Hilgert, J. and Neeb, K.-H.: LieGruppen und LieAlgebren, Vieweg, Braunschwieg (1991).

  • [Sch] Schoen, C.: Hodge classes on selfproducts of a variety with an automorphism, Compositio Math.65 (1988) 3-32.

    Google Scholar 

  • [vG] vanGeemen, B.: An introduction to the Hodge conjecture for Abelian varieties, in Algebraic Cycles and Hodge Theory, Torino, Lect. Notes in Math.1594 (1994) 233-252.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schoen, C. Addendum to: Hodge Classes on Self-Products of a Variety with an Automorphism. Compositio Mathematica 114, 321–328 (1998). https://doi.org/10.1023/A:1000566205021

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1000566205021

Navigation