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Intersection theory and heights : birational perspective
Multi angle
Authors : Chambert-Loir, Antoine (Author of the conference)
CIRM (Publisher )
11-XX - Number theory
14-XX - Algebraic geometry
37-XX - dynamical system - ergodic theory
CIRM (Publisher )
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Abstract :
The preceding Etats de la recherche on this topic happened in Rennes, 2006, and the organizers of the present edition asked me to make the bridge between these two sessions. My 2006 talks were devoted to the theory of heights and equidistribution theorems for algebraic dynamical systems. I will start from there by presenting the framework allowed by Arakelov geometry, and explaining the recent manuscript of X. Yuan and S.-W. Zhang who provide a birational perspective to these concepts. The theory is a bit complex and technical but I will try to emphasize the parallel between those ideas and the ones that lie at the ground of pluripotential theory in complex analysis, or in the theory of b-divisors in algebraic geometry.
Keywords : Arakelov geometry; birational geometry; complex geometry; heights; pluripotential
MSC Codes : Keywords : Arakelov geometry; birational geometry; complex geometry; heights; pluripotential
11-XX - Number theory
14-XX - Algebraic geometry
37-XX - dynamical system - ergodic theory
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 10/02/2025 Conference Date : 20/01/2025 Subseries : Research School arXiv category : Algebraic Geometry ; Number Theory Mathematical Area(s) : Dynamical Systems & ODE ; Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:07:21 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-01-20_Chambert-Loir.mp4 
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Information on the Event
Event Title : Etats de la recherche: Arithmetic, Algebraic and Analytics Dynamics / Etats de la recherche: Dynamique arithmétique, algébrique, et analytiqueEvent Organizers : Favre, Charles ; Gauthier, Thomas ; Raissy, Jasmin Dates : 20/01/2025 - 24/01/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3211.html
Citation Data
DOI : 10.24350/CIRM.V.20289903Cite this video as: Chambert-Loir, Antoine (2025). Intersection theory and heights : birational perspective. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20289903 URI : http://dx.doi.org/10.24350/CIRM.V.20289903 |
See Also
- [Virtualconference] Complexity theory in arithmetic dynamical systems - Lecture 3 / Author of the conference Xie, Junyi.
- [Virtualconference] Complexity theory in arithmetic dynamical systems - Lecture 2 / Author of the conference Xie, Junyi.
- [Multi angle] Degeneration of rational maps and hyperbolic components Lecture 3 / Author of the conference Luo, Yusheng.
- [Multi angle] Degeneration of rational maps and hyperbolic components - Lecture 2 / Author of the conference Luo, Yusheng.
- [Multi angle] The group of tame automorphisms - Lecture 3 / Author of the conference Lamy, Stéphane.
- [Multi angle] the group of tame automorphisms - Lecture 2 / Author of the conference Lamy, Stéphane.
- [Multi angle] Geometry and algebra of preperiodic points in $ \mathbb{P}^{N}$ - Lecture 3 / Author of the conference Demarco, Laura.
- [Multi angle] Geometry and algebra of preperiodic points in $ \mathbb{P}^{N}$ - Lecture 2 / Author of the conference Demarco, Laura.
- [Virtualconference] Complexity theory in arithmetic dynamical systems - Lecture 1 / Author of the conference Xie, Junyi.
- [Multi angle] Degeneration of rational maps and hyperbolic components - Lecture 1 / Author of the conference Luo, Yusheng.
- [Multi angle] the group of tame automorphisms - Lecture 1 / Author of the conference Lamy, Stéphane.
- [Multi angle] Geometry and algebra of preperiodic points in $ \mathbb{P}^{N}$ - Lecture 1 / Author of the conference Demarco, Laura.
- [Multi angle] Rigidity and examples / Author of the conference Cantat, Serge.
Bibliography
- CHAMBERT-LOIR, Antoine. Théorèmes d'équidistribution pour les syst\emes dynamiques d'origine arithmétique. arXiv preprint arXiv:0812.0944, 2008. - https://doi.org/10.48550/arXiv.0812.0944
- CANTAT, Serge, CHAMBERT-LOIR, Antoine, et GUEDJ, Vincent. Quelques aspects des systèmes dynamiques polynomiaux. Société mathématique de France, 2010. - https://smf.emath.fr/publications/quelques-aspects-des-systemes-dynamiques-polynomiaux
- YUAN, Xinyi et ZHANG, Shou-Wu. Adelic line bundles on quasi-projective varieties. arXiv preprint arXiv:2105.13587, 2021. - https://doi.org/10.48550/arXiv.2105.13587
