Bertini and Northcott
RESEARCH IN NUMBER THEORY(2021)
Abstract
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 .
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Key words
Bertini,Northcott,Height,Abelian varieties
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