Results 51 to 60 of about 4,610 (199)

Factor-4 and 6 compression of cyclotomic subgroups of and

Journal of Mathematical Cryptology, 2010
Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields 𝔽2m and 𝔽3m, respectively, have been used to implement pairing-based cryptographic protocols.
Karabina Koray
doaj   +1 more source

The geometry and arithmetic of bielliptic Picard curves

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
wiley   +1 more source

The growth of Tate–Shafarevich groups of p$p$‐supersingular elliptic curves over anticyclotomic Zp${\mathbb {Z}}_p$‐extensions at inert primes

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Let E$E$ be an elliptic curve defined over Q${\mathbb {Q}}$, and let K$K$ be an imaginary quadratic field. Consider an odd prime p$p$ at which E$E$ has good supersingular reduction with ap(E)=0$a_p(E)=0$ and which is inert in K$K$. Under the assumption that the signed Selmer groups are cotorsion modules over the corresponding Iwasawa algebra ...
Erman Işik, Antonio Lei
wiley   +1 more source

The 2‐divisibility of divisors on K3 surfaces in characteristic 2

Mathematische Nachrichten, Volume 298, Issue 6, Page 1964-1988, June 2025.
Abstract We show that K3 surfaces in characteristic 2 can admit sets of n$n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each n=8,12,16,20$n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only n=
Toshiyuki Katsura, Shigeyuki Kondō, Matthias Schütt   +2 more
wiley   +1 more source

On supersingular elliptic curves and hypergeometric functions [PDF]

Involve, a Journal of Mathematics, 2012
The Legendre family of elliptic curves has the remarkable property that both its periods and its supersingular locus have descriptions in terms of the hypergeometric function [math] . In this work we study elliptic curves and elliptic integrals with respect to the hypergeometric functions [math] and [math] , and prove that the supersingular [math ...
openaire   +2 more sources

Arithmetic Satake compactifications and algebraic Drinfeld modular forms

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract In this article, we construct the arithmetic Satake compactification of the Drinfeld moduli schemes of arbitrary rank over the ring of integers of any global function field away from the level structure, and show that the universal family extends uniquely to a generalized Drinfeld module over the compactification.
Urs Hartl, Chia‐Fu Yu
wiley   +1 more source

Quantitative upper bounds related to an isogeny criterion for elliptic curves

Bulletin of the London Mathematical Society, Volume 56, Issue 8, Page 2661-2679, August 2024.
Abstract For E1$E_1$ and E2$E_2$ elliptic curves defined over a number field K$K$, without complex multiplication, we consider the function FE1,E2(x)${\mathcal {F}}_{E_1, E_2}(x)$ counting nonzero prime ideals p$\mathfrak {p}$ of the ring of integers of K$K$, of good reduction for E1$E_1$ and E2$E_2$, of norm at most x$x$, and for which the Frobenius ...
Alina Carmen Cojocaru, Auden Hinz, Tian Wang   +2 more
wiley   +1 more source

The Endomorphism Rings of Supersingular Elliptic Curves over $\mathbb{F}_p$ and the Binary Quadratic Forms [PDF]

, 2022
Guanju Xiao, Zijian Zhou, Yingpu Deng, Longjiang Qu   +3 more
openalex   +1 more source

K3 surfaces of Kummer type in characteristic two

Bulletin of the London Mathematical Society, Volume 56, Issue 6, Page 1903-1919, June 2024.
Abstract We discuss K3 surfaces in characteristic two that contain the Kummer configuration of smooth rational curves.
Igor V. Dolgachev
wiley   +1 more source

On singular moduli that are S-units

, 2020
Recently Yu. Bilu, P. Habegger and L. K\"uhne proved that no singular modulus can be a unit in the ring of algebraic integers. In this paper we study for which sets S of prime numbers there is no singular modulus that is an S-units.
Campagna, Francesco
core   +1 more source