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math.NT2020
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.
math.NT2020
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…