English
Failure of the Brauer-Manin obstruction for a simply connected fourfold, and an orbifold version of the Mordell theorem
Post-edited
Auteurs : Kebekus, Stefan (Auteur de la Conférence)
CIRM (Editeur )
11G35 - Varieties over global fields
14F22 - Brauer groups of schemes
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 : 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
11G35 - Varieties over global fields
14F22 - Brauer groups of schemes
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 17/12/2019 Date de captation : 25/11/2019 Sous collection : Research talks arXiv category : Algebraic Geometry ; Number Theory Domaine : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 00:51:18 Audience : Researchers Download : https://videos.cirm-math.fr/2019-11-25_Kebekus.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Algebraic Geometry and Complex Geometry / Géométrie algébrique et géométrie complexeOrganisateurs 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
Données de citation
DOI : 10.24350/CIRM.V.19580903Citer cette vidéo: 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
- [Multi angle] The essential skeletons of pairs and the geometric P=W conjecture / Auteur de la Conférence Mauri, Mirko.
- [Multi angle] Representation varieties of fundamental groups of complex algebraic varieties and mixed Hodge structures / Auteur de la Conférence Lefèvre, Louis-Clément.
- [Multi angle] Rational curves on K3 surfaces / Auteur de la Conférence Gounelas, Frank.
- [Multi angle] Momentum polytopes of Kähler compact multiplicity-free manifolds / Auteur de la Conférence Cupit-Foutou, Stéphanie.
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
