TY - UNPB

T1 - p-adic adelic metrics and Quadratic Chabauty I

AU - Besser, Amnon

AU - Steffen Müller, J.

AU - Srinivasan, Padmavathi

PY - 2021/12/1

Y1 - 2021/12/1

N2 - We give a new construction of p-adic heights on varieties over number
fields using p-adic Arakelov theory. In analogy with Zhang's
construction of real-valued heights in terms of adelic metrics, these
heights are given in terms of p-adic adelic metrics on line bundles. In
particular, we describe a construction of canonical p-adic heights an
abelian varieties and we show that, for Jacobians, this recovers the
height constructed by Coleman and Gross. Our main application is a new
and simplified approach to the Quadratic Chabauty method for the
computation of rational points on certain curves over the rationals, by
pulling back the canonical height on the Jacobian with respect to a
carefully chosen line bundle.

AB - We give a new construction of p-adic heights on varieties over number
fields using p-adic Arakelov theory. In analogy with Zhang's
construction of real-valued heights in terms of adelic metrics, these
heights are given in terms of p-adic adelic metrics on line bundles. In
particular, we describe a construction of canonical p-adic heights an
abelian varieties and we show that, for Jacobians, this recovers the
height constructed by Coleman and Gross. Our main application is a new
and simplified approach to the Quadratic Chabauty method for the
computation of rational points on certain curves over the rationals, by
pulling back the canonical height on the Jacobian with respect to a
carefully chosen line bundle.

KW - Mathematics - Number Theory

KW - Mathematics - Algebraic Geometry

M3 - Preprint

BT - p-adic adelic metrics and Quadratic Chabauty I

ER -