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Algebraicity of polyquadratic plectic points
Multi angle
Authors : Gehrmann, Lennart (Author of the conference)
CIRM (Publisher )
11F41 - "Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, See also {14J20}"
11F67 - Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
11G05 - Elliptic curves over global fields
11G40 - $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
CIRM (Publisher )
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Abstract :
I will report on a plectic generalization of Stark-Heegner points. Inspired by Nekovar and Scholl's conjectures, these points are expected to control Mordell-Weil groups of higher rank elliptic curves. I will give strong evidence for this expectation in the case of polyquadratic CM fields. This is joint work with Michele Fornea.
Keywords : elliptic curves, rational points, p-adic methods
MSC Codes : Keywords : elliptic curves, rational points, p-adic methods
11F41 - "Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, See also {14J20}"
11F67 - Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
11G05 - Elliptic curves over global fields
11G40 - $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 25/07/2022 Conference Date : 20/06/2022 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 01:00:25 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-06-20_Gehrmann.mp4 
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Information on the Event
Event Title : Galois Representations, Automorphic Forms and L-Functions / Représentations galoisiennes, formes automorphes et leurs fonctions LEvent Organizers : Benois, Denis ; Dimitrov, Mladen ; Lang, Jaclyn ; Wiese, Gabor Dates : 20/06/2022 - 24/06/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2552.html
Citation Data
DOI : 10.24350/CIRM.V.19934903Cite this video as: Gehrmann, Lennart (2022). Algebraicity of polyquadratic plectic points. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19934903 URI : http://dx.doi.org/10.24350/CIRM.V.19934903 |
See Also
- [Multi angle] Smoothness of eigenvarieties and BSD for abelian surfaces / Author of the conference Loeffler, David.
- [Multi angle] Brumer-Stark units and a conjecture of Gross / Author of the conference Kakde, Mahesh.
- [Multi angle] A factorisation ZBK= (0,∞) ⊗ (0,∞) of Beilinson-Kato's system / Author of the conference Colmez, Pierre.
- [Multi angle] On the geometry of deformation rings and the Taylor-Wiles hypothesis / Author of the conference Allen, Patrick.
Bibliography
- FORNEA, Michele et GEHRMANN, Lennart. Plectic Stark-Heegner points. arXiv preprint arXiv:2104.12575, 2021. - https://doi.org/10.48550/arXiv.2104.12575
- FORNEA, Michele, GUITART, Xavier, et MASDEU, Marc. Plectic p-adic invariants. Advances in Mathematics, 2022, vol. 406, p. 108484. - https://doi.org/10.1016/j.aim.2022.108484
- FORNEA, Michele et GEHRMANN, Lennart. On the algebraicity of polyquadratic plectic points. arXiv preprint arXiv:2203.15998, 2022. - https://doi.org/10.48550/arXiv.2203.15998
- HERNÁNDEZ, Víctor et MOLINA, Santiago. Plectic points and Hida-Rankin p-adic L-functions. arXiv preprint arXiv:2202.12573, 2022. - https://doi.org/10.48550/arXiv.2202.12573
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