On the ordinary Hecke algebra
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.
scientific article; zbMATH DE number 89650
scientific article