Results 101 to 110 of about 10,181 (241)

Asymptotic Fermat's last theorem for a family of equations of signature (2,2n,n)$(2, 2n, n)$

Mathematika, Volume 70, Issue 4, October 2024.
Abstract In this paper, we study the integer solutions of a family of Fermat‐type equations of signature (2,2n,n)$(2, 2n, n)$, Cx2+qky2n=zn$Cx^2 + q^ky^{2n} = z^n$. We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant BC,q$B_{C, q}$ such that if n>BC,q$n > B_{C,q}$, there are no solutions (x,y ...
Pedro‐José Cazorla García
wiley   +1 more source

Essential dimension of isogenies

Pure and Applied Mathematics Quarterly
We give a lower bound for the essential dimension of isogenies of complex abelian varieties. The bound is sharp in many cases. In particular, the multiplication-by-$m$ map is incompressible for every $m\geq 2$, confirming a conjecture of Brosnan.
Kollár, János, Zhuang, Ziquan
openaire   +2 more sources

Cyclic isogenies and nonstandard arithmetic

Journal of Number Theory, 1980
AbstractFor a prime N we denote by X0(N)(K) the set of K-rational points on the modul curve of elliptic curves with isogenies of degree N. We formulate arithmetical axioms for number fields K that imply finiteness properties of X0(N)(K). To prove the results we use the nonstandard version of the Siegel-Mahler theorem (A. Robinson and P.
openaire   +2 more sources

Mod p points on shimura varieties of parahoric level

Forum of Mathematics, Pi
We study the $\overline {\mathbb {F}}_{p}$ -points of the Kisin–Pappas integral models of Shimura varieties of Hodge type with parahoric level. We show that if the group is quasi-split, then every isogeny class contains the reduction of a CM point,
Pol van Hoften
doaj   +1 more source

Isogenies of Polynomial Formal Groups

Journal of Algebra, 1999
A polynomial formal group is a commutative \(n\) dimensional formal group law \(F(x, y) = (F_1(x, y),\dots , F_n(x, y))\) such that the power series in \(n\) variables \(F_i(x, y)\) are polynomials. For \(n=1\), examples are \(F(x, y) = x+y + cxy\). For \(n>1\) see \textit{L. Childs, C. Greither, D. J. Moss, J. Sauerberg} and \textit{K.
openaire   +2 more sources

Genus Two Isogeny Cryptography [PDF]

, 2019
We study \((\ell ,\ell )\)-isogeny graphs of principally polarised supersingular abelian surfaces (PPSSAS). The \((\ell ,\ell )\)-isogeny graph has cycles of small length that can be used to break the collision resistance assumption of the genus two isogeny hash function suggested by Takashima.
Flynn, E, Ti, Y
openaire   +2 more sources

Orienteering with One Endomorphism. [PDF]

Mathematica (N Y), 2023
Arpin S, Chen M, Lauter KE, Scheidler R, Stange KE, Tran HTN.   +5 more
europepmc   +1 more source

Isogeny classes of abelian varieties over finite fields [PDF]

, 1968
Taira Honda
openalex   +1 more source

Paving the Way for SQIsign: Toward Efficient Deployment on 32-bit Embedded Devices

Mathematics
The threat of quantum computing has spurred research into post-quantum cryptography. SQIsign, a candidate submitted to the standardization process of the National Institute of Standards and Technology, is emerging as a promising isogeny-based signature ...
Yue Hu, Shiyu Shen, Hao Yang, Weize Wang
doaj   +1 more source

Isogeny Restrictions of Irreducible Admissible Representations are Finite Direct Sums of Irreducible Admissible Representations [PDF]

, 1979
Allan J. Silberger
openalex   +1 more source