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José Burgos' variations of arithmetic intersection theory
Multi angle
Authors : Kramer, Jürg (Author of the conference)
CIRM (Publisher )
11F50 - Jacobi forms
11G18 - Arithmetic aspects of modular and Shimura varieties
14G35 - Modular and Shimura varieties
14G40 - Arithmetic varieties and schemes; Arakelov theory; heights
32U05 - plurisubharmonic functions and generalizations
CIRM (Publisher )
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Abstract :
In our talk we will give a panorama of José Burgos' contributions to various generalizations of the classical arithmetic intersection theory developed by Gillet and Soulé. It starts with the extension of Arakelov geometry allowing to incorporate logarithmically singular metrics with applications to Shimura varieties. Further generalizations include toric varieties as well as the most recent results about arithmetic intersections of arithmetic b-divisors with applications to mixed Shimura varieties including the theory of Siegel-Jacobi forms.
Keywords : Arithmetic intersections; adelic divisors; plurisubharmonic functions; relative mixed energy; Shimura varieties; mixed Shimura varieties; modular forms; Jacobi forms
MSC Codes : Keywords : Arithmetic intersections; adelic divisors; plurisubharmonic functions; relative mixed energy; Shimura varieties; mixed Shimura varieties; modular forms; Jacobi forms
11F50 - Jacobi forms
11G18 - Arithmetic aspects of modular and Shimura varieties
14G35 - Modular and Shimura varieties
14G40 - Arithmetic varieties and schemes; Arakelov theory; heights
32U05 - plurisubharmonic functions and generalizations
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 17/11/2023 Conference Date : 11/10/2023 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : PDE ; Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:00:50 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-11_kramer.mp4 
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Information on the Event
Event Title : Global invariants of arithmetic varieties / Invariants globaux des variétés arithmétiquesEvent Organizers : Botero, Ana ; Freixas Montplet, Gérard ; Navarro Garmendia, Alberto ; Sombra, Martin Dates : 09/10/2023 - 13/10/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2857.html
Citation Data
DOI : 10.24350/CIRM.V.20102103Cite this video as: Kramer, Jürg (2023). José Burgos' variations of arithmetic intersection theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20102103 URI : http://dx.doi.org/10.24350/CIRM.V.20102103 |
See Also
- [Multi angle] Eisenstein K3 surfaces, equivariant analytic torsion, and automorphic forms on complex balls / Author of the conference Yoshikawa, Ken-Ichi.
- [Multi angle] Torsion points of elliptic curves via Berkovich spaces over $\mathbb{Z}$ / Author of the conference Poineau, Jérôme.
- [Multi angle] Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated / Author of the conference Botero, Ana.
- [Multi angle] On harmonic weak Maass forms associated to even integer weight newforms / Author of the conference Alfes-Neumann, Claudia.
Bibliography
- GIL, José I. Burgos, KRAMER, Jürg, et KÜHN, Ulf. Arithmetic characteristic classes of automorphic vector bundles. Documenta Mathematica, 2005, vol. 10, p. 619-716. - https://www.mathematik.hu-berlin.de/~kramer/doc_math_version.pdf
- DARVAS, Tamás, DI NEZZA, Eleonora, et LU, Chinh H. Monotonicity of nonpluripolar products and complex Monge–Ampère equations with prescribed singularity. Analysis & PDE, 2018, vol. 11, no 8, p. 2049-2087. - https://doi.org/10.2140/apde.2018.11.2049
- YUAN, Xinyi et ZHANG, Shou-Wu. Adelic line bundles over quasi-projective varieties. arXiv preprint arXiv:2105.13587, 2021. - https://arxiv.org/abs/2105.13587
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