6 papers
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.
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…
On the supersingular GPST attack
Andrea Basso, Fabien Pazuki
We explain why the first Galbraith-Petit-Shani-Ti attack on the Supersingular Isogeny Diffie-Hellman and the Supersingular Isogeny Key Encapsulation fails in some cases.
Heights and isogenies of Drinfeld modules
Florian Breuer, Fabien Pazuki, Mahefason Heriniaina Razafinjatovo
We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an expli…
Regulators of elliptic curves
Pascal Autissier, Marc Hindry, Fabien Pazuki
We study the regulator of the Mordell-Weil group of elliptic curves over number fields, functions fields of characteristic zero or function fields of characteristic . We prove…