22 citations · 51 across the 14 of their papers we have counts for
20 papers
Northcott numbers for the house and the Weil height
Fabien Pazuki, Niclas Technau, Martin Widmer
For an algebraic number and , be the (logarithmic) Weil height, and be the -weighted (logarithmic) Weil height of .…
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…
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…
Modular invariants and isogenies
Fabien Pazuki
We provide explicit bounds on the difference of heights of the -invariants of isogenous elliptic curves defined over . The first one is reminiscent of a c…
Abelian Calabi-Yau threefolds: Néron models and rational points
Fedor Bogomolov, Lars Halvard Halle, Fabien Pazuki +1
We study Calabi-Yau threefolds fibered by abelian surfaces, in particular, their arithmetic properties, e.g., Néron models and Zariski density.
Bornes sur le nombre de points rationnels des courbes -- en quete d'uniformite
Fabien Pazuki
The aim of this paper is to show how a conjectural lower bound on the canonical height function in the spirit of Lang and Silverman leads to an explicit uniform bound on the number…
Bad reduction of genus curves with CM jacobian varieties
Philipp Habegger, Fabien Pazuki
We show that a genus curve over a number field whose jacobian has complex multiplication will usually have stable bad reduction at some prime. We prove this by computing the Fa…
Heights, ranks and regulators of abelian varieties
Fabien Pazuki
We lower bound the Faltings height of an abelian variety over a number field by the sum of its injectivity diameter and the norm of its bad reduction primes. It leads to an uncondi…
Heights and regulators of number fields and elliptic curves
Fabien Pazuki
We compare general inequalities between invariants of number fields and invariants of abelian varieties over number fields. On the number field side, we remark that there is only a…
Rational points on curves over function fields
Amilcar Pacheco, Fabien Pazuki
We provide in this paper an upper bound for the number of rational points on a curve defined over a one variable function field over a finite field. The bound only depends on the c…
Décompositions en hauteurs locales
Fabien Pazuki
Let A be the jacobian variety of a hyperelliptic curve defined over a number field k. We provide a decomposition formula for the Faltings height of A and for the Néron-Tate height…
Polarized morphisms between abelian varieties
Fabien Pazuki
We study in this paper some criterions to get polarized morphisms between abelian varieties. We deduce explicit dynamical systems with particular intersection properties.
Zhang's conjecture and squares of abelian surfaces
F. Pazuki
We give in this paper some squares of abelian surfaces that are counterexamples to a conjecture formulated by Zhang about the intersection of subvarieties and preperiodic points.
Theta height and Faltings height
F. Pazuki
Using original ideas from J.-B. Bost and S. David, we provide an explicit comparison between the Theta height and the stable Faltings height of a principally polarized abelian vari…
Elementary 3-descent with a 3-isogeny
Henri Cohen, Fabien Pazuki
In this expository paper, we show how to use in practice 3-descent with a 3-isogeny to find an estimate for the rank of an elliptic curve having a rational 3-torsion subgroup, and…