Results 41 to 50 of about 1,931 (172)
Heights on ‘hybrid orbits’ in Shimura varieties
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract We prove the ‘hybrid conjecture’ which is a common generalisation of the André–Oort conjecture and the André–Pink–Zannier conjecture, in the case of Shimura varieties of abelian type.
Rodolphe Richard, Andrei Yafaev
wiley +1 more source
Quantum Money from Abelian Group Actions [PDF]
TheoretiCSWe give a construction of public key quantum money, and even a strengthened version called quantum lightning, from abelian group actions, which can in turn be constructed from suitable isogenies over elliptic curves.
Mark Zhandry
doaj +1 more source
Hash functions from superspecial genus-2 curves using Richelot isogenies
Journal of Mathematical Cryptology, 2020 In 2018 Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed over a quadratic finite field 𝔽p2.
Castryck Wouter +2 more
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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 +1 more
wiley +1 more source
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
The Open Book Series, 2013 The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper recounts the theory behind these graphs and examines several recently developed algorithms that ...
openaire +2 more sources
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 +3 more
wiley +1 more source
On the quaternion -isogeny path problem [PDF]
LMS Journal of Computation and Mathematics, 2014 AbstractLet $\mathcal{O}$ be a maximal order in a definite quaternion algebra over $\mathbb{Q}$ of prime discriminant $p$, and $\ell $ a small prime. We describe a probabilistic algorithm which, for a given left $\mathcal{O}$-ideal, computes a representative in its left ideal class of $\ell $-power norm.
Kohel, David +3 more
openaire +6 more sources
Abelian threefolds with imaginary multiplication
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract Let A$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
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
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