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H 2 Avoiding Jacobians

Auteurs : Masser, David (Auteur de la Conférence)
CIRM (Editeur )

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abelian variety isogeny Jacobian variety
Chai-Oort question
André-Oort complex multiplication Galois generic isogeny estimates Pila-Wilkie endomorphism estimates questions from the audience

Résumé : It is classical that, for example, there is a simple abelian variety of dimension $4$ which is not the jacobian of any curve of genus $4$, and it is not hard to see that there is one defined over the field of all algebraic numbers $\overline{\bf Q}$. In $2012$ Chai and Oort asked if there is a simple abelian fourfold, defined over $\overline{\bf Q}$, which is not even isogenous to any jacobian. In the same year Tsimerman answered ''yes''. Recently Zannier and I have done this over the rationals $\bf Q$, and with ''yes, almost all''. In my talk I will explain ''almost all'' the concepts involved.

Codes MSC :
11G10 - Abelian varieties of dimension >1
14H40 - Jacobians, Prym varieties
14K02 - Isogeny
14K15 - Arithmetic ground fields

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 29/05/2018
    Date de captation : 23/05/2018
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:57:28
    Domaine : Algebraic & Complex Geometry ; Number Theory
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-05-23_Masser.mp4

Informations sur la rencontre

Nom de la rencontre : Diophantine geometry / ​Géométrie diophantienne
Organisateurs de la rencontre : Bosser, Vincent ; Carrizosa, Maria ; Gaudron, Eric ; Habegger, Philipp
Dates : 21/05/2018 - 25/05/2018
Année de la rencontre : 2018
URL Congrès : https://conferences.cirm-math.fr/1754.html

Citation Data

DOI : 10.24350/CIRM.V.19408303
Cite this video as: Masser, David (2018). Avoiding Jacobians. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19408303
URI : http://dx.doi.org/10.24350/CIRM.V.19408303

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