Brauer-Siegel for arithmetic tori and lower bounds for Galois orbits of special points

DOI10.1090/S0894-0347-2012-00739-5zbMath1362.11057arXiv1103.5619MaRDI QIDQ5326483

Jacob Tsimerman

Publication date: 6 August 2013

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.5619

zbMATH Keywords

discriminantGalois orbitsarithmetic toriBrauer-Siegel formula

Mathematics Subject Classification ID

Complex multiplication and moduli of abelian varieties (11G15) Arithmetic aspects of modular and Shimura varieties (11G18) Arithmetic ground fields for abelian varieties (14K15)

Related Items (17)

Unlikely Intersections with ExCM curves in A2 ⋮ About the mixed André-Oort conjecture: reduction to a lower bound for the pure case ⋮ The hyperbolic Ax-Lindemann-Weierstraß conjecture ⋮ Heights of pre-special points of Shimura varieties ⋮ Bounded equidistribution of special subvarieties in mixed Shimura varieties ⋮ Towards the André-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points ⋮ The André-Oort conjecture for \(\mathcal A_g\) ⋮ On the distribution of the Hodge locus ⋮ Lower bounds for Galois orbits of special points on Shimura varieties: a point-counting approach ⋮ Ax-Lindemann for \(\mathcal{A}_g\) ⋮ Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves ⋮ Heuristics and conjectures in the direction of a $p$-adic Brauer–Siegel Theorem ⋮ Galois representations attached to abelian varieties of CM type ⋮ The André–Oort conjecture for the moduli space of abelian surfaces ⋮ Reflection principles for class groups ⋮ Effective André-Oort conjecture for non-compact curves in Hilbert modular varieties ⋮ Nombre de classes des tores de multiplication complexe et bornes inférieures pour les orbites Galoisiennes de points spéciaux

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• Arithmetic of algebraic tori
• On the Tamagawa number of algebraic tori
• Ranks of 3-class groups of non-Galois cubic fields
• Nombre de classes des tores de multiplication complexe et bornes inférieures pour les orbites Galoisiennes de points spéciaux
• Reflection Principles and Bounds for Class Group Torsion
• Open problems in algebraic geometry

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