Overconvergent Eichler-Shimura isomorphisms for quaternionic modular forms over Q
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ProjectBSD - Euler systems and the conjectures of Birch and Swinnerton-Dyer, Bloch and Kato (EC-H2020-682152)
In this work we construct overconvergent Eichler-Shimura isomorphisms over Shimura curves over Q. More precisely, for a prime p > 3 and a wide open disk U in the weight space, we construct a Hecke-Galois-equivariant morphism from the space of families of overconvergent modular symbols over U to the space of families of overconvergent modular forms over U . In addition, for all but finitely many weights λ ∈ U , this morphism provides a description of the finite slope part of the space of overconvergent modular symbols of weight λ in terms of the finite slope part of the space of overconvergent modular forms of weight λ + 2. Moreover, for classical weights these overconvergent isomorphisms are compatible with the classical Eichler-Shimura isomorphism.
CitationBarrera, D., Gao, S. Overconvergent Eichler-Shimura isomorphisms for quaternionic modular forms over Q. "International journal of number theory", 1 Novembre 2017, vol. 13, núm. 10, p. 2684-2712.