English
José Burgos' variations of arithmetic intersection theory
Multi angle
Auteurs : Kramer, Jürg (Auteur de la Conférence)
CIRM (Editeur )
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 (Editeur )
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Résumé :
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
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de publication : 17/11/2023 Date de captation : 11/10/2023 Sous collection : Research talks arXiv category : Number Theory Domaine : PDE ; Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Durée : 01:00:50 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-11_kramer.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Global invariants of arithmetic varieties / Invariants globaux des variétés arithmétiquesOrganisateurs de la rencontre : Botero, Ana ; Freixas Montplet, Gérard ; Navarro Garmendia, Alberto ; Sombra, Martin Dates : 09/10/2023 - 13/10/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2857.html
Données de citation
DOI : 10.24350/CIRM.V.20102103Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Eisenstein K3 surfaces, equivariant analytic torsion, and automorphic forms on complex balls / Auteur de la Conférence Yoshikawa, Ken-Ichi.
- [Multi angle] Torsion points of elliptic curves via Berkovich spaces over $\mathbb{Z}$ / Auteur de la Conférence Poineau, Jérôme.
- [Multi angle] Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated / Auteur de la Conférence Botero, Ana.
- [Multi angle] On harmonic weak Maass forms associated to even integer weight newforms / Auteur de la Conférence Alfes-Neumann, Claudia.
Bibliographie
- 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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