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Lehmer without Bogomolov
Fabien Pazuki, Niclas Technau, Martin Widmer
We construct fields of algebraic numbers that have the Lehmer property but not the Bogomolov property. This answers a recent implicit question of Pengo and the first author.
On the Northcott property for special values of L-functions
Fabien Pazuki, Riccardo Pengo
We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of L-functions. We first introduce an axiomatic approach to these three properties.…
Bertini and Northcott
Fabien Pazuki, Martin Widmer
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…
Isogenies of elliptic curves over function fields
Richard Griffon, Fabien Pazuki
We prove two theorems concerning isogenies of elliptic curves over function fields. The first one describes the variation of the height of the -invariant in an isogeny class. Th…