Français
Avoiding Jacobians
Post-edited
Authors : Masser, David (Author of the conference)
CIRM (Publisher )
11G10 - Abelian varieties of dimension >1
14H40 - Jacobians, Prym varieties
14K02 - Isogeny
14K15 - Arithmetic ground fields
CIRM (Publisher )
Abstract :
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.
MSC Codes : 11G10 - Abelian varieties of dimension >1
14H40 - Jacobians, Prym varieties
14K02 - Isogeny
14K15 - Arithmetic ground fields
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 29/05/2018 Conference Date : 23/05/2018 Subseries : Research talks arXiv category : Number Theory ; Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:57:28 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-05-23_Masser.mp4 
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Information on the Event
Event Title : Diophantine geometry / Géométrie diophantienneEvent Organizers : Bosser, Vincent ; Carrizosa, Maria ; Gaudron, Eric ; Habegger, Philipp Dates : 21/05/2018 - 25/05/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1754.html
Citation Data
DOI : 10.24350/CIRM.V.19408303Cite 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 |
See Also
- [Post-edited] Stable models for modular curves in prime level / Author of the conference Parent, Pierre.
- [Multi angle] Shimura curves and bounds for the $abc$ conjecture / Author of the conference Pasten, Hector.
- [Multi angle] A new Northcott property for Faltings height / Author of the conference Mocz, Lucia.
- [Multi angle] Recent progress in the classification of torsion subgroups of elliptic curves / Author of the conference Lozano-Robledo, Alvaro.
Bibliography
- 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
