Displaying similar documents to “The Mordell–Lang question for endomorphisms of semiabelian varieties”

The optimality of the Bounded Height Conjecture

Evelina Viada (2009)

Journal de Théorie des Nombres de Bordeaux

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In this article we show that the Bounded Height Conjecture is optimal in the sense that, if V is an irreducible subvariety with empty deprived set in a power of an elliptic curve, then every open subset of V does not have bounded height. The Bounded Height Conjecture is known to hold. We also present some examples and remarks.

On uniform lower bound of the Galois images associated to elliptic curves

Keisuke Arai (2008)

Journal de Théorie des Nombres de Bordeaux

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Let p be a prime and let K be a number field. Let ρ E , p : G K → Aut ( T p E ) ≅ GL 2 ( ℤ p ) be the Galois representation given by the Galois action on the p -adic Tate module of an elliptic curve E over K . Serre showed that the image of ρ E , p is open if E has no complex multiplication. For an elliptic curve E over K whose j -invariant does not appear in an exceptional finite set (which is non-explicit however), we give an explicit uniform lower bound of the size of the image of ρ E , p .

Proof of the Knop conjecture

Ivan V. Losev (2009)

Annales de l’institut Fourier

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In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoid are equivariantly isomorphic. We also state and prove a uniqueness property for (not necessarily smooth) affine spherical varieties.