Differential modular forms over totally real fields of integral weights

In this article, we construct a differential modular form of non-zero order and integral weight for compact Shimura curves over totally real fields bigger than Q . The construction uses the theory of lifting ordinary mod p Hilbert modular forms to characteristic 0 as well as the theory of Igusa curv...

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Bibliographic Details
Published inResearch in number theory Vol. 7; no. 3
Main Authors Banerjee, Debargha, Saha, Arnab
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2021
Springer Nature B.V
Subjects
Analytic functions
Curves
Integrals
Mathematics
Mathematics and Statistics
Modular construction
Modular structures
Number Theory
Research in Number Theory
Primary: 13F35
adic Modular forms
Deformation theory
11F41
Secondary: 11F32
14D15
Witt vectors
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Summary:In this article, we construct a differential modular form of non-zero order and integral weight for compact Shimura curves over totally real fields bigger than Q . The construction uses the theory of lifting ordinary mod p Hilbert modular forms to characteristic 0 as well as the theory of Igusa curve. This is the analogue of the construction of Buium in the case of modular curves parametrizing elliptic curves with level structures.
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-021-00269-7