Results 41 to 50 of about 5,346 (174)
Modular invariants and isogenies [PDF]
, 2019 We provide explicit bounds on the difference of heights of the $j$-invariants of isogenous elliptic curves defined over $\overline{\mathbb{Q}}$. The first one is reminiscent of a classical estimate for the Faltings height of isogenous abelian varieties ...
Pazuki, Fabien
core +2 more sources
Horizontal Racewalking Using Radical Isogenies
, 2022 sponsorship: This work was supported in part by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement ISOCRYPT -No. 101020788) and by CyberSecurity Research Flanders with reference number VR20192203.
Castryck, Wouter +3 more
openaire +2 more sources
Ordinary primes for GL2$\operatorname{GL}_2$‐type abelian varieties and weight 2 modular forms
Mathematika, Volume 72, Issue 2, April 2026.Abstract Let A$A$ be a g$g$‐dimensional abelian variety defined over a number field F$F$. It is conjectured that the set of ordinary primes of A$A$ over F$F$ has positive density, and this is known to be true when g=1,2$g=1, 2$, or for certain abelian varieties with extra endomorphisms.
Tian Wang, Pengcheng Zhang
wiley +1 more source
Isogenies of Elliptic Curves: A Computational Approach [PDF]
, 2009 Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the reducibility of ...
Shumow, Daniel
core +2 more sources
Exhibiting Sha[2] on hyperelliptic jacobians [PDF]
, 2006 We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves, with an emphasis on the theory and practice of visualisation.
Bruin, N., Flynn, E. V.
core +4 more sources
Algebraic Geometry, 2016 We prove by means of the study of the infinitesimal variation of Hodge structure and a generalization of the classical Babbage-Enriques-Petri theorem that the Jacobian variety of a generic element of a $k$ codimensional subvariety of $\mathcal M_g$ is not isogenous to a distinct Jacobian if $g>3k+4$.
Marcucci, Valeria +2 more
openaire +7 more sources
Graph potentials and topological quantum field theories
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans +2 more
wiley +1 more source
Vector bundles on bielliptic surfaces: Ulrich bundles and degree of irrationality
Mathematische Nachrichten, Volume 299, Issue 3, Page 514-528, March 2026.Abstract This paper deals with two problems about vector bundles on bielliptic surfaces. The first is to give a classification of Ulrich bundles on such surfaces S$S$, which depends on the topological type of S$S$. In doing so, we study the weak Brill–Noether property for moduli spaces of sheaves with isotropic Mukai vector. Adapting an idea of Moretti
Edoardo Mason
wiley +1 more source
Optimization of isogeny computation algorithms for post-quantum cryptography
Scientific AfricanIsogeny-based cryptography has emerged as a strong candidate for post-quantum security due to the believed hardness of finding isogenies between supersingular elliptic curves.
Mohammed El Baraka, Siham Ezzouak
doaj +1 more source
Quantum Money from Abelian Group Actions [PDF]
TheoretiCSWe give a construction of public key quantum money, and even a strengthened version called quantum lightning, from abelian group actions, which can in turn be constructed from suitable isogenies over elliptic curves.
Mark Zhandry
doaj +1 more source