2021/02/25 by Juan Esteban Rodríguez Camargo, Camargo, Juan Esteban Rodríguez
Agricultural and Biological Sciences · Mathematics · #Algebraic Geometry and Number Theory #Bryophyte Studies and Records #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2102.13099
openalex publication_date 2021/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a new proof of Faltings's p-adic Eichler-Shimura decomposition of the modular curves via BGG methods and the Hodge-Tate period map. The key property is the relation between the Tate module and the Faltings extension, which was already used in the original proof. Then, we construct overconvergent Eichler-Shimura (ES) maps for the modular curves providing ''the second half'' of the overconvergent ES map of Andreatta-Iovita-Stevens. We use higher Coleman theory on the modular curve developed by Boxer-Pilloni to show that the small slope part of the ES maps interpolates the classical p-adic Eichler-Shimura decompositions. Finally, we prove that the overconvergent ES maps are compatible with Poincaré and Serre pairings.