Results 61 to 70 of about 6,385 (201)

On families of K3 surfaces with real multiplication

Forum of Mathematics, Sigma
We exhibit large families of K3 surfaces with real multiplication, both abstractly, using lattice theory, the Torelli theorem and the surjectivity of the period map, as well as explicitly, using dihedral covers and isogenies.
Bert van Geemen, Matthias Schütt
doaj   +1 more source

The $3$-isogeny Selmer groups of the elliptic curves $y^2=x^3+n^2$ [PDF]

, 2022
Stephanie Chan
openalex   +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

Spectra of subrings of cohomology generated by characteristic classes for fusion systems

Bulletin of the London Mathematical Society, Volume 57, Issue 7, Page 1990-2005, July 2025.
Abstract If F$\mathcal {F}$ is a saturated fusion system on a finite p$p$‐group S$S$, we define the Chern subring Ch(F)${\operatorname{Ch}}(\mathcal {F})$ of F$\mathcal {F}$ to be the subring of H∗(S;Fp)$H^*(S;{\mathbb {F}}_p)$ generated by Chern classes of F$\mathcal {F}$‐stable representations of S$S$. We show that Ch(F)${\operatorname{Ch}}(\mathcal {
Ian J. Leary, Jason Semeraro
wiley   +1 more source

On the Parallelization of Square-Root Vélu’s Formulas

Mathematical and Computational Applications
A primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies.
Jorge Chávez-Saab, Odalis Ortega, Amalia Pizarro-Madariaga   +2 more
doaj   +1 more source

Supersingular K3 Surfaces are Unirational

, 2014
We show that supersingular K3 surfaces in characteristic $p\geq5$ are related by purely inseparable isogenies. This implies that they are unirational, which proves conjectures of Artin, Rudakov, Shafarevich, and Shioda.
Liedtke, Christian
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

Isogenies on Kummer Surfaces

Mathematics of Computation
We first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient ( N , N ) (N,N) -isogenies, for any odd  N N , both on the general Kummer surface and on the Fast model.
Corte-Real Santos, M, Flynn, EV
openaire   +2 more sources

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

Explicit classification of isogeny graphs of rational elliptic curves [PDF]

, 2022
Alexander J. Barrios
openalex   +1 more source