Results 81 to 90 of about 5,346 (174)

On isogeny classes of Edwards curves over finite fields [PDF]

, 2011
We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a {\em complete} Edwards curve, and that an Edwards curve is ...
Ahmadi, Omran, Granger, Robert
core   +1 more source

Hyperelliptic Jacobians and isogenies

, 2018
Motivated by results of Mestre and Voisin, in this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians In the first part we prove that a very general hyperelliptic Jacobian of genus $g\ge 4$ is not isogenous to a non ...
Naranjo, Juan Carlos, Pirola, Gian Pietro   +1 more
core   +1 more source

Hasse principle for Kummer varieties in the case of generic 2‐torsion

Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.
Abstract Conditional on finiteness of relevant Shafarevich–Tate groups, Harpaz and Skorobogatov used Swinnerton‐Dyer's descent‐fibration method to establish the Hasse principle for Kummer varieties associated to a 2‐covering of a principally polarised abelian variety under certain largeness assumptions on its mod 2 Galois image.
Adam Morgan
wiley   +1 more source

Parabolic subgroups in characteristics 2 and 3

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract This text brings to an end the classification of non‐reduced parabolic subgroups in positive characteristic, especially 2 and 3: they are all obtained as intersections of parabolics having maximal reduced part. We prove this result and deduce a few geometric consequences on rational projective homogeneous varieties.
Matilde Maccan
wiley   +1 more source

An effective Arakelov-theoretic version of the hyperbolic isogeny theorem

, 2015
For an integer $e$ and hyperbolic curve $X$ over $\overline{\mathbb Q}$, Mochizuki showed that there are only finitely many isomorphism classes of hyperbolic curves $Y$ of Euler characteristic $e$ with the same universal cover as $X$.
Javanpeykar, Ariyan
core   +1 more source

Strong subgroup recurrence and the Nevo–Stuck–Zimmer theorem

Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.
Abstract Let Γ$\Gamma$ be a countable group and Sub(Γ)$\mathrm{Sub}(\Gamma)$ its Chabauty space, namely, the compact Γ$\Gamma$‐space consisting of all subgroups of Γ$\Gamma$. We call a subgroup Δ∈Sub(Γ)$\Delta \in \mathrm{Sub}(\Gamma)$ a boomerang subgroup if for every γ∈Γ$\gamma \in \Gamma$, γniΔγ−ni→Δ$\gamma ^{n_i} \Delta \gamma ^{-n_i} \rightarrow ...
Yair Glasner, Waltraud Lederle
wiley   +1 more source

Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories

SciPost Physics
We study how the global structure of rank-one 4d $\mathcal{N}=2$ supersymmetric field theories is encoded into global aspects of the Seiberg-Witten elliptic fibration.
Cyril Closset, Horia Magureanu
doaj   +1 more source

Oblivious signature based on the theory of elliptic curve isogeny

Научно-технический вестник информационных технологий, механики и оптики
This paper presents a novel 1-out-of-n post-quantum oblivious signature scheme based on supersingular elliptic curve isogenies. The proposed scheme is built upon the Commutative Supersingular Isogeny based Fiat-Shamir scheme whose security relies on the ...
A. F. Khutsaeva
doaj   +1 more source

Isogeny graphs and Isogeny Volcanoes

, 2020
\textit{Isogeny graphs} are a type of graphs, where the vertices represent elliptic curves and the edges represent isogenies. I will examine some of the structures of these graphs in this thesis. It turns out that the majority of the components of such a graph will be \textit{volcanoes}, see \cref{defn:pvolcano}.
openaire   +1 more source

Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves

Cryptography
The article presents the author’s works in the field of modifications and modeling of the Post-Quantum Cryptography (PQC) Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) algorithm on non-cyclic supersingular Edwards curves and its predecessor ...
Anatoly Bessalov, Volodymyr Sokolov, Serhii Abramov   +2 more
doaj   +1 more source