Results 61 to 70 of about 8,681 (237)
Computing endomorphism rings of abelian varieties of dimension two [PDF]
, 2012 Generalizing a method of Sutherland and the author for elliptic curves, we design a subexponential algorithm for computing the endomorphism rings of ordinary abelian varieties of dimension two over finite fields.
Bisson, Gaetan
core +5 more sources
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
A Compact and Scalable Hardware/Software Co-design of SIKE
Transactions on Cryptographic Hardware and Embedded Systems, 2020 We present efficient and compact hardware/software co-design implementations of the Supersingular Isogeny Key Encapsulation (SIKE) protocol on field-programmable gate arrays (FPGAs).
Pedro Maat C. Massolino +3 more
doaj +1 more source
A local-global principle for isogenies of prime degree over number fields
, 2014 We give a description of the set of exceptional pairs for a number field $K$, that is the set of pairs $(\ell, j(E))$, where $\ell$ is a prime and $j(E)$ is the $j$-invariant of an elliptic curve $E$ over $K$ which admits an $\ell$-isogeny locally almost
Anni, Samuele
core +2 more sources
Efficient computation of (2n,2n)-isogenies
Des. Codes Cryptogr.Elliptic curves are abelian varieties of dimension one; the two-dimensional analogues are abelian surfaces. In this work we present an algorithm to compute $$(2^n,2^n)$$ ( 2 n , 2 n ) -isogenies between abelian surfaces defined over ...
S. Kunzweiler
semanticscholar +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
Elliptic curves in isogeny classes [PDF]
Journal of Number Theory, 2018 We show that the distribution of elliptic curves in isogeny classes of curves with a given value of the Frobenius trace $t$ becomes close to uniform even when $t$ is averaged over very short intervals inside the Hasse-Weil interval.
Igor E. Shparlinski, Liangyi Zhao
openaire +3 more sources
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
Renormalization, Isogenies, and Rational Symmetries of Differential Equations
Advances in Mathematical Physics, 2010 We give an example of infinite-order rational transformation that leaves a linear differential equation covariant. This example can be seen as a nontrivial but still simple illustration of an exact representation of the renormalization group.
A. Bostan +6 more
doaj +1 more source
Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem [PDF]
, 2017 Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multiplication.
Jetchev, Dimitar, Wesolowski, Benjamin
core +1 more source