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Overconvergent Eichler-Shimura Isomorphisms on Shimura Curves over a Totally Real Field

Title:

Overconvergent Eichler-Shimura Isomorphisms on Shimura Curves over a Totally Real Field

Gao, Shan (2016) Overconvergent Eichler-Shimura Isomorphisms on Shimura Curves over a Totally Real Field. PhD thesis, Concordia University.

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Abstract

In this work we construct overconvergent Eichler-Shimura isomorphisms on Shimura curves
over a totally real field F. More precisely, for a prime p > 2 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 isomorphisms.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (PhD)
Authors:Gao, Shan
Institution:Concordia University
Degree Name:Ph. D.
Program:Mathematics
Date:8 September 2016
Thesis Supervisor(s):Iovita, Adrian
ID Code:981729
Deposited By: SHAN GAO
Deposited On:09 Nov 2016 19:03
Last Modified:18 Jan 2018 17:53
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