$p$-adic ordinary Hecke algebras for $\mathrm{GL}\left(2\right)$

Hida, Haruzo. "$p$-adic ordinary Hecke algebras for ${\rm GL}(2)$." Annales de l'institut Fourier 44.5 (1994): 1289-1322. <http://eudml.org/doc/75098>.

@article{Hida1994,
abstract = {We study the $p$-adic nearly ordinary Hecke algebra for cohomological modular forms on $GL(2)$ over an arbitrary number field $F$. We prove the control theorem and the independence of the Hecke algebra from the weight. Thus the Hecke algebra is finite over the Iwasawa algebra of the maximal split torus and behaves well under specialization with respect to weight and $p$-power level. This shows the existence and the uniqueness of the (nearly ordinary) $p$-adic analytic family of cohomological Hecke eigenforms parametrized by the algebro-geometric spectrum of the Hecke algebra. As for a size of the algebra, we make a conjecture which predicts the Krull dimension of the Hecke algebra. This conjecture implies the Leopoldt conjecture for $F$ and its quadratic extensions containing a $CM$ field. We conclude the paper studying some special cases where the conjecture holds under the hypothesis of the Leopoldt conjecture for $F$ and $p$.},
author = {Hida, Haruzo},
journal = {Annales de l'institut Fourier},
keywords = {-adic nearly ordinary Hecke algebra; weight; -power level; cohomological Hecke eigenforms; Krull dimension; Leopoldt conjecture},
language = {eng},
number = {5},
pages = {1289-1322},
publisher = {Association des Annales de l'Institut Fourier},
title = {$p$-adic ordinary Hecke algebras for $\{\rm GL\}(2)$},
url = {http://eudml.org/doc/75098},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Hida, Haruzo
TI - $p$-adic ordinary Hecke algebras for ${\rm GL}(2)$
JO - Annales de l'institut Fourier
PY - 1994
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 5
SP - 1289
EP - 1322
AB - We study the $p$-adic nearly ordinary Hecke algebra for cohomological modular forms on $GL(2)$ over an arbitrary number field $F$. We prove the control theorem and the independence of the Hecke algebra from the weight. Thus the Hecke algebra is finite over the Iwasawa algebra of the maximal split torus and behaves well under specialization with respect to weight and $p$-power level. This shows the existence and the uniqueness of the (nearly ordinary) $p$-adic analytic family of cohomological Hecke eigenforms parametrized by the algebro-geometric spectrum of the Hecke algebra. As for a size of the algebra, we make a conjecture which predicts the Krull dimension of the Hecke algebra. This conjecture implies the Leopoldt conjecture for $F$ and its quadratic extensions containing a $CM$ field. We conclude the paper studying some special cases where the conjecture holds under the hypothesis of the Leopoldt conjecture for $F$ and $p$.
LA - eng
KW - -adic nearly ordinary Hecke algebra; weight; -power level; cohomological Hecke eigenforms; Krull dimension; Leopoldt conjecture
UR - http://eudml.org/doc/75098
ER -