Results 11 to 20 of about 10,181 (241)
Modular Isogeny Complexes [PDF]
Algebraic & Geometric Topology, 2011 We describe a vanishing result on the cohomology of a cochain complex associated to the moduli of chains of finite subgroup schemes on elliptic curves. These results have applications to algebraic topology, in particular to the study of power operations ...
Rezk, Charles
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AN ISOGENY OF K3 SURFACES [PDF]
Bulletin of the London Mathematical Society, 2006 In a recent paper Ahlgren, Ono and Penniston described the L-series of K3 surfaces from a certain one parameter family in terms of those of a particular family of elliptic curves. The Tate conjecture predicts the existence of a correspondence between these K3 surfaces and certain Kummer surfaces related to these elliptic curves.
Bert van Geemen, J. Top
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Journal of High Energy Physics, 2021 AbstractWe consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a number of ways, including Feynman parametrization, lightcone and Baikov (in full and loop-by-loop variants).
Frellesvig, Hjalte +3 more
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Comptes Rendus. MathématiqueIn this paper, we apply Tsuzuki’s main theorem in [12] to establish a criterion for when two abelian varieties over a function field $K$ of characteristic $p$ are isogenous. Specifically, assuming that their endomorphism algebras tensored with $\mathbb{Q}
Chiarellotto, Bruno, Trihan, Fabien
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Algebraic Geometry, 2016 We prove by means of the study of the infinitesimal variation of Hodge structure and a generalization of the classical Babbage-Enriques-Petri theorem that the Jacobian variety of a generic element of a $k$ codimensional subvariety of $\mathcal M_g$ is not isogenous to a distinct Jacobian if $g>3k+4$.
Marcucci, Valeria +2 more
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Torsion point attacks on ‘SIDH‐like’ cryptosystems
IET Information Security, 2023 Isogeny‐based cryptography is a promising approach for post‐quantum cryptography. The best‐known protocol following that approach is the supersingular isogeny Diffie–Hellman protocol (SIDH); this protocol was turned into the CCA‐secure key encapsulation ...
Péter Kutas, Christophe Petit
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, 2020 sponsorship: This work was supported in part by the Research Council KU Leuven grants C14/18/067 and STG/17/019, by CyberSecurity Research Flanders with reference number VR20192203, and by the Research Foundation Flanders (FWO) through the WOG Coding Theory and Cryptography. (Research Council KU Leuven|C14/18/067, Research Council KU Leuven|STG/17/019,
Castryck, Wouter +2 more
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Review of Chosen Isogeny-Based Cryptographic Schemes
Cryptography, 2022 Public-key cryptography provides security for digital systems and communication. Traditional cryptographic solutions are constantly improved, e.g., to suppress brute-force attacks.
Bartosz Drzazga, Łukasz Krzywiecki
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Hyperelliptic Jacobians and isogenies [PDF]
Advances in Mathematics, 2018 Motivated by results of Mestre and Voisin, in this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians In the first part we prove that a very general hyperelliptic Jacobian of genus $g\ge 4$ is not isogenous to a non-hyperelliptic Jacobian.
Naranjo, J. C., Pirola, G. P.
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