Avoiding Jacobians | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Chapitres

Avoiding Jacobians

De David Masser

Apparaît dans la collection : Diophantine geometry / Géométrie diophantienne

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.

Informations sur la vidéo

Date de captation 23/05/2018
Date de publication 29/05/2018
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19408303
Citer cette vidéo Masser, David (23/05/2018). Avoiding Jacobians. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19408303
URL https://dx.doi.org/10.24350/CIRM.V.19408303

Domaine(s)

Bibliographie

Chai, Ching-Li; Oort, Frans (2012). Abelian varieties isogenous to a Jacobian. Ann. Math. (2) 176, No. 1, 589-635 - https://doi.org/10.4007/annals.2012.176.1.11
Masser, D.W., & Wüstholz, G. (1994). Endomorphism estimates for abelian varieties. Mathematische Zeitschrift, 215(4), 641-653 - https://doi.org/10.1007/BF02571735
Tsimerman, J. (2012). Brauer-Siegel for arithmetic tori and lower bounds for Galois orbits of special points. Journal of the American Mathematical Society, 25(4), 1091-1117 - https://doi.org/10.1090/S0894-0347-2012-00739-5
Tsimerman, J. (2012). The existence of an abelian variety over $\overline{\bf Q}$ isogenous to no Jacobian. Annals of Mathematics, 176(1), 637-650 - https://doi.org/10.4007/annals.2012.176.1.12

Codes MSC

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2025

Donner son avis