Results 61 to 70 of about 4,610 (199)
Picard sheaves, local Brauer groups, and topological modular forms
Journal of Topology, Volume 17, Issue 2, June 2024.Abstract We develop tools to analyze and compare the Brauer groups of spectra such as periodic complex and real K$K$‐theory and topological modular forms, as well as the derived moduli stack of elliptic curves. In particular, we prove that the Brauer group of TMF$\mathrm{TMF}$ is isomorphic to the Brauer group of the derived moduli stack of elliptic ...
Benjamin Antieau +2 more
wiley +1 more source
Endomorphism algebras of QM abelian surfaces
, 2013 We determine endomorphism algebras of abelian surfaces with quaternion multiplication.Comment: 14 pages.
Yu, Chia-Fu
core +1 more source
A survey on post‐quantum based approaches for edge computing security
WIREs Computational Statistics, Volume 16, Issue 1, January/February 2024.The distribution of reviewed papers by focused area. Abstract With the development of technology and its integration with scientific realities, computer systems continue to evolve as infrastructure. One of the most important obstacles in front of quantum computers with high‐speed processing is that its existing systems cause security vulnerabilities ...
Aykut Karakaya, Ahmet Ulu
wiley +1 more source
Kida's formula and congruences [PDF]
, 2005 We prove a formula (analogous to that of Kida in classical Iwasawa theory and generalizing that of Hachimori-Matsuno for elliptic curves) giving the analytic and algebraic p-adic Iwasawa invariants of a modular eigenform over an abelian p-extension of Q ...
Pollack, Robert, Weston, Tom
core +3 more sources
On random sampling of supersingular elliptic curves
Annali di Matematica Pura ed Applicata (1923 -)Abstract We consider the problem of sampling random supersingular elliptic curves over finite fields of cryptographic size (SRS problem). The currently best-known method combines the reduction of a suitable complex multiplication (CM) elliptic curve and a random walk over some supersingular isogeny graph.
Mula, Marzio +2 more
openaire +3 more sources
Pairing Optimizations for Isogeny‐Based Cryptosystems
IET Information Security, Volume 2024, Issue 1, 2024.In isogeny‐based cryptography, bilinear pairings are regarded as a powerful tool in various applications, including key compression, public key validation, and torsion basis generation. However, in most isogeny‐based protocols, the performance of pairing computations is unsatisfactory due to the high computational cost of the Miller function.
Shiping Cai +3 more
wiley +1 more source
Generic Newton polygons for curves of given p-rank [PDF]
, 2013 We survey results and open questions about the $p$-ranks and Newton polygons of Jacobians of curves in positive characteristic $p$. We prove some geometric results about the $p$-rank stratification of the moduli space of (hyperelliptic) curves.
Achter, Jeff, Pries, Rachel
core
Generalization of Atkin’s orthogonal polynomials and supersingular elliptic curves [PDF]
Proceedings of the American Mathematical Society, 2012 In a 1998 paper, Kaneko and Zagier explain unpublished work of Atkin which exhibits an infinite sequence of polynomials with the property that when suitable polynomials are reduced mod p p for a prime p p , one gets the locus of supersingular elliptic curves.
openaire +2 more sources
THE ANTICYCLOTOMIC MAIN CONJECTURE FOR ELLIPTIC CURVES AT SUPERSINGULAR PRIMES [PDF]
Journal of the Institute of Mathematics of Jussieu, 2007 The Main Conjecture of Iwasawa theory for an elliptic curve is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by Perrin-Riou, Pollack, Kurihara, Kobayashi and Iovita and Pollack are required to handle this case in which many of the simplifying features of the ordinary setting break down.
IOVITA, ADRIAN, DARMON H.
openaire +2 more sources
Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22
, 2015 In this note we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes p congruent 3 mod 4 in a systematic way.
Brandhorst, Simon
core +1 more source