Intersection theory and heights : birational perspective | Vidéo | Carmin.tv

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Intersection theory and heights : birational perspective

By Antoine Chambert-Loir

Appears in collection : Etats de la recherche: Arithmetic, Algebraic and Analytics Dynamics / Etats de la recherche: Dynamique arithmétique, algébrique, et analytique

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.

Information about the video

Date of recording 20/01/2025
Date of publication 10/02/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20289903
Cite this video Chambert-Loir, Antoine (20/01/2025). Intersection theory and heights : birational perspective. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20289903
URL https://dx.doi.org/10.24350/CIRM.V.20289903

Domain(s)

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

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