Integral Hodge theory and congruences between modular forms
type: Item
instance of: scholarly article
title: Integral Hodge theory and congruences between modular forms
zbMATH Open document ID: 0851.11032
DOI: 10.1215/S0012-7094-95-08017-X
author: Bruce W. Jordan
author: Ron Livné
published in: Duke Mathematical Journal
publication date: 1996-11-25T00:00:00Z
review text: The authors offer a new perspective on the construction of fusion modules between new and old modular forms. They develop the Eckmann-Hodge theory for hermitian local systems over graphs and use it to study integral models of the symmetric power representations of a quaternion algebra over the rationals (Chapter 2). All this is necessary in constructing a module of fusion \(\Phi\) between the automorphic forms of a definite quaternion algebra (Chapter 3, especially Theorem 3.25). Transferring \(\Phi\) to a module of fusion between forms on \(GL(2)\) one obtains a module of fusion for classical modular forms (Corollary 4.11). An application to congruences between modular forms is given (Theorem 4.12).
reviewed by: Andrzej Dąbrowski
Mathematics Subject Classification ID: 11F33
Mathematics Subject Classification ID: 14C30
zbMATH DE Number: 878420
zbMATH Keywords: integral Hodge theory
zbMATH Keywords: construction of fusion modules
zbMATH Keywords: modular forms
zbMATH Keywords: symmetric power representations of a quaternion algebra
zbMATH Keywords: congruences between modular forms
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 878420