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H 2 Failure of the Brauer-Manin obstruction for a simply connected fourfold, and an orbifold version of the Mordell theorem

Auteurs : Kebekus, Stefan (Auteur de la Conférence)
CIRM (Editeur )

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Simply connected surfaces over global fields Failure of the Hasse principle Mordell theorem for orbifold curves Height bounds

Résumé : Almost one decade ago, Poonen constructed the first examples of algebraic varieties over global fields for which Skorobogatov’s etale Brauer-Manin obstruction does not explain the failure of the Hasse principle. By now, several constructions are known, but they all share common geometric features such as large fundamental groups.
This talk discusses a construction of simply connected fourfolds over global fields of positive characteristic for which the Brauer-Manin machinery fails. Contrary to earlier work in this direction, our construction does not rely on major conjectures. Instead, we establish a new diophantine result of independent interest: a Mordell-type theorem for Campana’s "geometric orbifolds" over function fields of positive characteristic. Along the way, we also construct the first example of simply connected surface of general type over a global field with a non-empty, but non-Zariski dense set of rational points.
Joint work with Pereira and Smeets.

Keywords : Brauer-Manin obstruction, Hasse principle, orbifold, Mordell-type theorem

Codes MSC :
11G35 - Varieties over global fields
14F22 - Brauer groups of schemes

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 17/12/2019
    Date de captation : 25/11/2019
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:51:18
    Domaine : Algebraic & Complex Geometry
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2019-11-25_Kebekus.mp4

Informations sur la rencontre

Nom de la rencontre : Algebraic Geometry and Complex Geometry / Géométrie algébrique et géométrie complexe
Organisateurs de la rencontre : Benoist, Olivier ; Floris, Enrica
Dates : 25/11/2019 - 29/11/2019
Année de la rencontre : 2019
URL Congrès : https://conferences.cirm-math.fr/2074.html

Citation Data

DOI : 10.24350/CIRM.V.19580903
Cite this video as: Kebekus, Stefan (2019). Failure of the Brauer-Manin obstruction for a simply connected fourfold, and an orbifold version of the Mordell theorem. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19580903
URI : http://dx.doi.org/10.24350/CIRM.V.19580903

Voir aussi

Bibliographie

  • KEBEKUS, Stefan, PEREIRA, Jorge Vitório, et SMEETS, Arne. Brauer-Manin failure for a simply connected fourfold over a global function field, via orbifold Mordell. arXiv preprint arXiv:1905.02795, 2019. - https://arxiv.org/abs/1905.02795



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