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A Bogomolov property for curves modulo algebraic subgroups

Philipp Habegger — 2009

Bulletin de la Société Mathématique de France

Generalizing a result of Bombieri, Masser, and Zannier we show that on a curve in the algebraic torus which is not contained in any proper coset only finitely many points are close to an algebraic subgroup of codimension at least $2$ . The notion of close is defined using the Weil height. We also deduce some cardinality bounds and further finiteness statements.

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