Theta height and Faltings height

By Fabien Pazuki. 2009

55 citations recorded by the source corpus.

Using original ideas from J.-B. Bost and S. David, we provide an explicit comparison between the Theta height and the stable Faltings height of a principally polarized abelian variety. We also give as an application an explicit upper bound on the number of K-rational points of a curve of genus g>1 over a number filed K under a conjecture of S. Lang and J. Silverman. We complete the study with a comparison between differential lattice structures.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/ab8e9288c7e5f13910786c9a4d058ed7116e8b1e

How researchers see this paper

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In Computational Theory and Mathematics

1. Ziyang Gao
2. P. Habegger
3. V. Dimitrov

In Geometry and Topology

1. Ziyang Gao
2. P. Habegger
3. V. Dimitrov
4. Jacob Tsimerman
5. Benjamin Bakker

In Sociology and Political Science

1. Ziyang Gao
2. P. Habegger
3. V. Dimitrov

Citations in the corpus

• Uniformity in Mordell–Lang for curves (2020, methodology): “The height h DP ( A g,τ ( s ) ) used by David and Philippon is bounded similarly by work of Bost and David, see [DP02, Corollaire 6.9] and [Paz12].”