On the p-adic distance between a point of finite order and a curve of genus higher or equal to two

2008/04/23 by Damian Rössler, Rössler, Damian · 1 citation
Computer Science · Mathematics · #14G40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0804.3747

openalex publication_date 2008/04/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

Let A be an abelian variety over \bf C_p (p a prime number) and V\hookrightarrow A a closed subvariety. The conjecture of Tate-Voloch predicts that the p-adic distance from a torsion point T\not∈ V(\bf C_p) to the variety V is bounded below by a strictly positive constant. This conjecture is proven by Hrushovski and Scanlon, when A has a model over \bf C_p. We give an explicit formula for this constant, in the case where V is a curve embedded into its Jacobian and V has a model over a number field. This explicit formula involves analytic and arakelovian invariants of the curve.

Cited by

• Torsion subschemes and the Tate-Voloch conjecture over p-adic fields

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