Bertini and Northcott

We prove a new Bertini-type Theorem with explicit control of the genus, degree, height, and the field of definition of the constructed curve. As a consequence we provide a general strategy to reduce certain height and rank estimates on abelian varieties over a number field K to the case of jacobian...

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Bibliographic Details
Published inResearch in number theory Vol. 7; no. 1
Main Authors Pazuki, Fabien, Widmer, Martin
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2021
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Number Theory
Abelian varieties
14K15
Height
11G50
14G40
Northcott
11G30
Bertini
11G10
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Summary:We prove a new Bertini-type Theorem with explicit control of the genus, degree, height, and the field of definition of the constructed curve. As a consequence we provide a general strategy to reduce certain height and rank estimates on abelian varieties over a number field K to the case of jacobian varieties defined over a suitable extension of K .
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-021-00236-2