Globally analytic p-adic representations of the pro--p--Iwahori subgroup of GL(2) and base change‎, ‎I‎ : ‎Iwasawa algebras and a base change map

Abstract. This paper extends to the pro-p Iwahori subgroup of GL(2) over an unramified finite extension of Qp the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of SL(2, Zp). It then describes a natural base change map between the Iwasawa algebras or more correctly, as it turns out, between the global distribution algebras on the associated rigid-analytic spaces. In a forthcoming paper this will be applied to p-adic representation theory.