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Overconvergent Eichler-Shimura isomorphisms for unitary Shimura curves over totally real fields

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Abstract

We compare two different cohomology groups on unitary Shimura curves over totally real number fields; these groups are used in the construction of p-adic families of modular forms in this context. More precisely, we describe the space of finite slope overconvergent modular forms of any weight in terms of a convenient overconvergent cohomology.

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Acknowledgments

It is a great pleasure to thank Adrian Iovita for his support, encouragement and generosity. We would also like to thank Riccardo Brasca, Vincent Pilloni, Fabrizio Andreatta and Adel Betina for their interest and helpful discussions.

The first author has received funding from the CRM in Montreal, the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 682152) and from the FONDECYT PAI 77180007. The second author is supported by NNSF of China (grant number 11601136) and Joint Fund Project of Local Universities in Yunnan Province (grant number 2017FH001-122).

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Authors and Affiliations

  1. Universidad de Santiago de Chile, Alameda 3363, Santiago, Chile

    Daniel Barrera

  2. Department of Mathematics, Honghe University, Mengzi, Yunnan, 661199, China

    Shan Gao

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  1. Daniel Barrera
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  2. Shan Gao
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Correspondence to Daniel Barrera.

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Barrera, D., Gao, S. Overconvergent Eichler-Shimura isomorphisms for unitary Shimura curves over totally real fields. Isr. J. Math. 242, 707–767 (2021). https://doi.org/10.1007/s11856-021-2143-z

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  • DOI: https://doi.org/10.1007/s11856-021-2143-z

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