Publications related to Height function

Some Mordell-Weil lattices and applications to sphere packings

We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields.In some cases, these families of elliptic curves ...

EPFL2024

Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

Serge Vaudenay, Bénédikt Minh Dang Tran

Witness encryption is a cryptographic primitive which encrypts a message under an instance of an NP language and decrypts the ciphertext using a witness associated with that instance. In the current state of the art, most of the witness encryption construc ...

Springer2023

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Gauthier Leterrier

We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) ...

SPRINGER INT PUBL AG2022

Serre-Tate theory for Calabi-Yau varieties

Maciej Emilian Zdanowicz

Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...

WALTER DE GRUYTER GMBH2021

Global Frobenius liftability I

Maciej Emilian Zdanowicz

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...

EUROPEAN MATHEMATICAL SOC-EMS2021

Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0

Zsolt Patakfalvi, Lei Zhang

Let k be an algebraically closed field of characteristic p > 0. We give a birational characterization of ordinary abelian varieties over k: a smooth projective variety X is birational to an ordinary abelian variety if and only if kappa(S)(X) = 0 and b(1)(X ...

DUKE UNIV PRESS2019

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

Some consequences of Masser's counting theorem on elliptic curves

Valéry Aurélien Mahé

We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...

Springer Heidelberg2017

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Height function

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Some Mordell-Weil lattices and applications to sphere packings

Moments of the number of points in a bounded set for number field lattices

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Serre-Tate theory for Calabi-Yau varieties

Global Frobenius liftability I

Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0

Arithmetic and geometric structures in cryptography

Some consequences of Masser's counting theorem on elliptic curves

Isogeny graphs of ordinary abelian varieties

Moments of the number of points in a bounded set for number field lattices

Some Mordell-Weil lattices and applications to sphere packings

Serre-Tate theory for Calabi-Yau varieties

Arithmetic and geometric structures in cryptography

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Some consequences of Masser's counting theorem on elliptic curves

Isogeny graphs of ordinary abelian varieties

Global Frobenius liftability I

Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0