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2 results

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

  • CHAD SCHOEN
  • Journal:
    Compositio Mathematica / Volume 114 / Issue 3 / December 1998
    Published online by Cambridge University Press:
    04 December 2007, pp. 321-328
    Print publication:
    December 1998
    • Article
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  • 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.

  • Duality on tori and multiplicative dependence relations

  • Part of
  • Daniel Bertrand
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 62 / Issue 2 / April 1997
    Published online by Cambridge University Press:
    09 April 2009, pp. 198-216
    Print publication:
    April 1997
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  • In this paper, we give multihomogeneous estimates for the group of relations linking multiplicatively dependent algebraic numbers. In the process, we raise a question in the style of Lehmer's problem, concerning multidimensional covolumes in the lattice of units. The proofs are based on the Brill-Gordan duality theorem on orthogonal lattices, and the paper closes with an algebraic version of the theorem, concerning orthogonal abelian subvarieties of an arbitrarily polarized abelian variety.