AG – Séminaire dématérialisé : Dimitri Koshelev (LMV) : Finite field mapping to elliptic curves of j-invariant 1728

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AG – Séminaire dématérialisé : Dimitri Koshelev (LMV) : Finite field mapping to elliptic curves of j-invariant 1728

19 mai 2020 / 11:00 - 12:00

In the report we will generalize the simplified Shallue–van de Woestijne–Ulas (SWU) method of a deterministic finite field mapping  F_q->E(F_q) to the case of any elliptic (F_q)-curve E of j-invariant 1728. More precisely, we will obtain a rational F_q-curve (and its explicit quite simple proper F_q-parametrization) on the Kummer surface K’ associated with the direct product ExE’, where E ‘ is the quadratic (F_q)-twist of E.  The simplified SWU method consists in computing the direct image of the parametrization and a subsequent inverse image (P,Q) of the natural two-sheeted covering ExE’->K’. Denoting by s:E’ -> E the corresponding  (F_{q^2})-isomorphism, it is easily seen that: P is in E(F_q) or s(Q)  belongs to  E(F_q).

 

 

 


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ID de réunion : 966 1345 6223 ; contacter Luc Pirio pour le mot de passe.

AG – Séminaire dématérialisé : Dimitri Koshelev (LMV) : Finite field mapping to elliptic curves of j-invariant 1728

Détails

Date :
19 mai 2020
Heure :
11:00 - 12:00
Catégorie d’évènement:

Organisateurs

Luc Pirio
Nicolas Perrin