2023
DOI: 10.1112/s0010437x23007182
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p-adic Eichler–Shimura maps for the modular curve

Abstract: We give a new proof of Faltings's $p$ -adic Eichler–Shimura decomposition of the modular curves via Bernstein–Gelfand–Gelfand (BGG) methods and the Hodge–Tate period map. The key property is the relation between the Tate module and the Faltings extension, which was used in the original proof. Then we construct overconvergent Eichler–Shimura maps for the modular curves providing ‘the second half’ of the overconvergent Eichler–Shimura map of Andreatta, Iovita and Stevens. We use higher… Show more

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