351 citations
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Showing 2003 · math.NTShow all
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math.NT2003
A Lower Bound for the Canonical Height on Abelian Varieties over Abelian Extensions
Matthew Baker, Joseph Silverman
Let A be an abelian variety defined over a number field K, and consider the canonical height function attached to a symmetric ample line bundle L on A. We prove that there is a pos…
math.NT2003
A lower bound for the canonical height on elliptic curves over abelian extensions
Joseph H. Silverman
Let E/K be an ellptic curve defined over a number field, let h be the canonical height on E, and let K^ab be the maximal abelian extension of K. Extending work of M. Baker, we prov…
math.NT2003★ 3 cited
Groupes fondamentaux motiviques de Tate mixte
P. Deligne, A. B. Goncharov
We define the category of mixed Tate motives over the ring of S-integers of a number field. We define the motivic fundamental group (made unipotent) of a unirational variety over a…