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5 papers · 1 filter
The Weil-Etale Topology for Number Rings
Stephen Lichtenbaum
We would like to construct a new Grothendieck topology for arithmetic schemes, whose cohomology groups associated with motivic complexes of sheaves are finitely generated and whose…
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…
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…
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…
Polylogarithms, regulators and Arakelov motivic complexes
A. B. Goncharov
We construct an explicit regulator map from the weigh n Bloch Higher Chow group complexto the weight n Deligne complex of a regular complex projective algebraic variety X. We defin…