-adic ordinary Hecke algebras for
We study the -adic nearly ordinary Hecke algebra for cohomological modular forms on over an arbitrary number field . 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 -power level. This shows the existence and the uniqueness of the (nearly ordinary) -adic analytic family of cohomological Hecke eigenforms...