Results 41 to 50 of about 3,064 (192)

Recognising flag varieties and reductive groups

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract Fix a flat and projective morphism X→Σ$X\rightarrow \Sigma$ of schemes. We show, first, that any set of P1${\mathbb {P}}^1$‐fibrations on X$X$ defines a set of simple roots, a set of simple coroots and a Cartan matrix C$C$. Second, X$X$ is an étale F${\mathcal {F}}$‐bundle over some projective Σ$\Sigma$‐scheme, where F${\mathcal {F}}$ is the ...
Ian Grojnowski, Nicholas Shepherd‐Barron   +1 more
wiley   +1 more source

Optimization of isogeny computation algorithms for post-quantum cryptography

Scientific African
Isogeny-based cryptography has emerged as a strong candidate for post-quantum security due to the believed hardness of finding isogenies between supersingular elliptic curves.
Mohammed El Baraka, Siham Ezzouak
doaj   +1 more source

SIKE Channels

Transactions on Cryptographic Hardware and Embedded Systems, 2022
We present new side-channel attacks on SIKE, the isogeny-based candidate in the NIST PQC competition. Previous works had shown that SIKE is vulnerable to differential power analysis, and pointed to coordinate randomization as an effective countermeasure.
Luca De Feo, Nadia El Mrabet, Aymeric Genêt, Novak Kaluđerovi´c, Natacha Linard de Guertechin, Simon Pontié, Élise Tasso   +6 more
doaj   +1 more source

Derived isogenies and isogenies for abelian surfaces

Algebra & Number Theory
In this paper, we study the twisted Fourier-Mukai partners of abelian surfaces. Following the work of Huybrechts [doi:10.4171/CMH/465], we introduce the twisted derived equivalence between abelian surfaces. We show that there is a twisted derived Torelli theorem for abelian surfaces over algebraically closed fields with characteristic $\neq 2,3$.
Li, Zhiyuan, Zou, Haitao
openaire   +2 more sources

On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
wiley   +1 more source

Extended supersingular isogeny Diffie–Hellman key exchange protocol: Revenge of the SIDH

IET Information Security, 2021
The supersingular isogeny Diffie–Hellman key exchange protocol (SIDH) was introduced by Jao and De Feo in 2011. SIDH operates on supersingular elliptic curves defined over Fp2, where p is a large prime number of the form p=4eA3eB−1 and eA and eB are ...
Daniel Cervantes‐Vázquez, Eduardo Ochoa‐Jiménez, Francisco Rodríguez‐Henríquez   +2 more
doaj   +1 more source

Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p$p$

Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.
Abstract Let G$G$ be a finite group and p$p$ be a prime. We establish an upper bound for the derived length of a Sylow p$p$‐subgroup of G$G$ in terms of the number of irreducible characters of G$G$ whose degrees are divisible by p$p$. We also prove that if B$B$ is a p$p$‐block of a finite p$p$‐solvable group G$G$ with defect group D$D$, then the ...
James P. Cossey, Mark L. Lewis, A. A. Schaeffer Fry, Hung P. Tong‐Viet   +3 more
wiley   +1 more source

Orientations and cycles in supersingular isogeny graphs [PDF]

, 2022
The paper concerns several theoretical aspects of oriented supersingular $\ell$-isogeny volcanoes and their relationship to closed walks in the supersingular $\ell$-isogeny graph.
Kristin E. Lauter, Ha T. N. Tran, Mingjie Chen, Renate Scheidler, Katherine Stange, Sarah Arpin   +5 more
core   +1 more source

Abelian threefolds with imaginary multiplication

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract Let A$A$ be an abelian threefold defined over a number field K$K$ with potential multiplication by an imaginary quadratic field M$M$. Under mild assumptions on K$K$, if A$A$ has signature (2,1) and the multiplication by M$M$ is defined over KM$KM$, we attach to A$A$ an elliptic curve defined over K$K$ with potential complex multiplication by M$
Francesc Fité, Pip Goodman
wiley   +1 more source

Prismatic F‐crystals and Wach modules

Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.
Abstract We show that the category of analytic/completed prismatic F-crystals$F\text{-crystals}$ on the absolute prismatic site of a small (unramified at p$p$) base ring is naturally equivalent to the category of relative Wach modules from the theory of (φ,Γ)-modules$(\varphi, \Gamma)\text{-modules}$.
Abhinandan
wiley   +1 more source