Linear representation of endomorphisms of Kummer varieties
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | LUBICZ, David | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | ROBERT, Damien | |
| dc.date.accessioned | 2024-04-04T02:46:39Z | |
| dc.date.available | 2024-04-04T02:46:39Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191574 | |
| dc.description.abstractEn | Let K A be a Kummer variety defined as the quotient of an Abelian variety A by the automorphism (−1) of A. Let T * 0 (A) be the co-tangent space at the point 0 of A. Let End(A) be the additive group of endomorphisms of A. There is a well defined map ρ : End(A) → Aut(T * 0 (A)), f → (df) * 0 , where (df) * 0 is the differential of f in 0 acting on T * 0 (A). The data of f ∈ End(K A) which comes from f ∈ End(A), determines ρ(f) up to a sign. The aim of this paper is to describe an efficient algorithm to recover ρ(f) up to a sign from the knowledge of f. Our algorithm is based on a study of the tangent cone of a Kummer variety in its singular 0 point. We give an application to Mestre's point counting algorithm. | |
| dc.description.sponsorship | Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008 | |
| dc.language.iso | en | |
| dc.title.en | Linear representation of endomorphisms of Kummer varieties | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03204365 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03204365v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=LUBICZ,%20David&ROBERT,%20Damien&rft.genre=preprint |
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