Heights on curves and limits of Hodge structures

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Spencer Bloch
  • Robin de Jong
  • Emre Can Sertöz

Research Organisations

External Research Organisations

  • University of Chicago
  • Leiden University
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Details

Original languageEnglish
Pages (from-to)340-361
Number of pages22
JournalJournal of the London Mathematical Society
Volume108
Issue number1
Publication statusPublished - 4 Jul 2023

Abstract

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.

ASJC Scopus subject areas

Cite this

Heights on curves and limits of Hodge structures. / Bloch, Spencer; de Jong, Robin; Sertöz, Emre Can.
In: Journal of the London Mathematical Society, Vol. 108, No. 1, 04.07.2023, p. 340-361.

Research output: Contribution to journal › Article › Research › peer review

Bloch S, de Jong R, Sertöz EC. Heights on curves and limits of Hodge structures. Journal of the London Mathematical Society. 2023 Jul 4;108(1):340-361. doi: 10.48550/arXiv.2206.01220, 10.1112/jlms.12747
Bloch, Spencer ; de Jong, Robin ; Sertöz, Emre Can. / Heights on curves and limits of Hodge structures. In: Journal of the London Mathematical Society. 2023 ; Vol. 108, No. 1. pp. 340-361.
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note = "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 Sch{\"u}tt for his valuable comments on our paper. We thank Raymond van Bommel, David Holmes and Steffen M{\"u}ller for helpful discussions. We also acknowledge the use of Magma [ 6 ] and SageMath [ 18 ] for facilitating experimentation. We thank {\"O}zde Bayer Sert{\"o}z and Ali Sinan Sert{\"o}z 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. ",
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