Theta height and Faltings height. (Hauteur Thêta et hauteur de Faltings.) (English. French summary) Zbl 1245.14029
Let \(A\) be a principally polarized abelian variety defined over a number field \(K\), where the principal polarization is defined by a fixed ample symmetric line bundle \(L\) on \(A\). The aim of the paper under review is to give an explicit comparison between the Theta height \(h_\Theta(A,L)\) and the stable Faltings height \(h_F(A)\) of \(A\). The original ideas are due to J.-B. Bost and S. David. As an application of this study, the author shows that an explicit Lang-Silverman inequality (Lang-Silverman’s conjecture, J. H. Silverman [Duke Math. J. 51, 395–403 (1984; Zbl 0579.14035)]) would give an explicit upper bound on the number of \(K\)-rational points on a curve of genus \(g\geq2\) independent of the height of the Jacobian of the curve.
Reviewer: Shun Tang (Bonn)
MSC:
| 14G40 | Arithmetic varieties and schemes; Arakelov theory; heights |
| 11G50 | Heights |
| 14G05 | Rational points |
Citations:
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