Bertini and Northcott

DOI10.1007/s40993-021-00236-2zbMath1466.11038arXiv2006.13604OpenAlexW3121131417MaRDI QIDQ2658343

Fabien Pazuki, Martin Widmer

Publication date: 19 March 2021

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.13604

zbMATH Keywords

heightabelian varietiesBertiniNorthcott

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Heights (11G50) Arithmetic ground fields for abelian varieties (14K15) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (2)

Northcott numbers for the house and the Weil height ⋮ Diophantine approximations. Abstracts from the workshop held April 17--23, 2022

Cites Work

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• The existence of an abelian variety over \(\overline{\mathbb{Q}}\) isogenous to no Jacobian
• Polarization and isogenies
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• The Galois groups of the polynomials \(X^ n+aX\ell +b\)
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• On infinite unramified extensions.
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• Semistable reduction and torsion subgroups of abelian varieties
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• Degree of definition of endomorphisms of an abelian variety
• Bounded ranks and Diophantine error terms
• Abelian varieties isogenous to no Jacobian
• Period theorem and minimal degrees of isogenies
• Quasi-functions and heights on abelian varieties
• Good reduction of abelian varieties
• A note on the Northcott property and undecidability
• Theta height and Faltings height
• Heights and regulators of number fields and elliptic curves
• Nombre de points rationnels des courbes
• On the irreducibility of certain trinomials
• Quasi-Equivalence of Heights and Runge’s Theorem
• A note on generators of number fields
• Décompositions en hauteurs locales
• Modeles de neron et monodromie

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