p-adic Eichler-Shimura theory - Lecture 2 | Vidéo | Carmin.tv

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p-adic Eichler-Shimura theory - Lecture 2

By George Boxer

Appears in collection : Jean Morlet Chair - Classical and p-adic aspects of the Kudla program / Chaire Jean Morlet - Aspects classiques et p-adiques du programme Kudla

Modular forms can be realized as Betti cohomology classes or coherent cohomology classes on modular curves. Eichler-Shimura theory compares both realizations. Using Betti realization, one can construct a first theory of p-adic automorphic forms : completed cohomology. Using the coherent realization we can construct another theory of p-adic automorphic forms : (higher) Coleman theory. Both theories compare, this is the p-adic Eichler-Shimura theory. In this course we will introduce several incarnations of the p-adic Shimura varieties (classical, perfectoid, locally analytic), as well as various period morphisms (Hodge-Tate and de Rham) and use this geometry to develop the theory of p-adic automorphic forms.

Information about the video

Date of recording 08/06/2026
Date of publication 06/07/2026
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20500403
Cite this video Boxer, George (08/06/2026). p-adic Eichler-Shimura theory - Lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20500403
URL https://dx.doi.org/10.24350/CIRM.V.20500403

Domain(s)

Number Theory

Bibliography

PAN, Lue. On locally analytic vectors of the completed cohomology of modular curves. In : Forum of Mathematics, Pi. Cambridge University Press, 2022. p. e7. - https://doi.org/10.1017/fmp.2022.1
CAMARGO, J. E. Locally analytic completed cohomology. arXiv preprint arXiv:2209.01057, 2022. - https://doi.org/10.48550/arXiv.2209.01057
JIANG, Yuanyang. Differential operators on locally analytic Shimura varieties. arXiv preprint arXiv:2604.09116, 2026. - https://doi.org/10.48550/arXiv.2604.09116
BOXER, George, CALEGARI, Frank, GEE, Toby, et al. Modularity theorems for abelian surfaces. arXiv preprint arXiv:2502.20645, 2025. - https://doi.org/10.48550/arXiv.2502.20645

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