On the ordinary Hecke algebra
type: Item
instance of: scholarly article
title: On the ordinary Hecke algebra
zbMATH Open document ID: 0774.11026
DOI: 10.1016/0022-314X(92)90119-A
author: Fernando Q. Gouvêa
published in: Journal of Number Theory
publication date: 1993-01-16T00:00:00Z
review text: This paper is related to the work of \textit{H. Hida} on the algebra of Hecke operators acting on ordinary \(p\)-adic modular forms [Invent. Math. 85, 545-613 (1986; Zbl 0612.10021); Ann. Sci. Ec. Norm. Supér., IV. Sér. 19, 231-273 (1986; Zbl 0607.10022)]. This algebra is finite and flat over the Iwasawa algebra \(\Lambda\cong \mathbb{Z}_ pT\), and it is related to Iwasawa theory and to Galois representations. The main purpose of the paper under review is to make explicit a few results on the structure of this algebra under certain hypotheses. One essential condition is that the weight of the modular forms should be \(\geq 3\). The author remarks that the fundamental ideas are all due to H. Hida. But it is obvious that the author had to add a large portion of own work to obtain his explicit results.
reviewed by: Hans Opolka
Mathematics Subject Classification ID: 11F85
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11F80
zbMATH DE Number: 89650
zbMATH Keywords: algebra of Hecke operators
zbMATH Keywords: \(p\)-adic modular forms
zbMATH Keywords: Iwasawa theory
zbMATH Keywords: Galois representations
MaRDI profile type: Publication
cites work: Q5607047
cites work: On the characteristic power series of the \(U\) operator
cites work: Galois representations into \(\text{GL}_2(\mathbb Z_pX)\) attached to ordinary cusp forms.
cites work: Iwasawa modules attached to congruences of cusp forms
cites work: A Study of the Local Components of the Hecke Algebra mod l
cites work: Congruences Between Systems of Eigenvalues of Modular Forms
cites work: Q3215315
cites work: Higher congruences between modular forms
cites work: Q4078156
cites work: \(p\)-adic interpolation of real analytic Eisenstein series
cites work: Newforms and functional equations
cites work: On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
cites work: Q3800159
cites work: A formula for Ramanujan's \(\tau\)-function
description: scientific article; zbMATH DE number 89650