TY - JOUR

T1 - Heights on curves and limits of Hodge structures

AU - Bloch, Spencer

AU - de Jong, Robin

AU - Sertöz, Emre Can

N1 - Funding Information: We thank all members of the International Groupe de Travail on differential equations in Paris for numerous valuable comments and their encouragement and, in particular, Vasily Golyshev, Matt Kerr, and Duco van Straten. We thank Greg Pearlstein for helpful discussions and sharing his notes on limits of height pairings with us. We thank Matthias Schütt for his valuable comments on our paper. We thank Raymond van Bommel, David Holmes and Steffen Müller for helpful discussions. We also acknowledge the use of Magma [ 6 ] and SageMath [ 18 ] for facilitating experimentation. We thank Özde Bayer Sertöz and Ali Sinan Sertöz for the pictures in the paper. The third author gratefully acknowledges support from MPIM Bonn. We thank the referee for a careful reading of the manuscript and insightful suggestions.

PY - 2023/7/4

Y1 - 2023/7/4

N2 - We exhibit a precise connection between Néron–Tate heights on smooth curves and biextension heights of limit mixed Hodge structures associated to smoothing deformations of singular quotient curves. Our approach suggests a new way to compute Beilinson–Bloch heights in higher dimensions.

AB - We exhibit a precise connection between Néron–Tate heights on smooth curves and biextension heights of limit mixed Hodge structures associated to smoothing deformations of singular quotient curves. Our approach suggests a new way to compute Beilinson–Bloch heights in higher dimensions.

UR - http://www.scopus.com/inward/record.url?scp=85157972370&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2206.01220

DO - 10.48550/arXiv.2206.01220

M3 - Article

AN - SCOPUS:85157972370

VL - 108

SP - 340

EP - 361

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 1

ER -