%0 Journal Article %T 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 %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Clozel, L. %D 2017 %\ 08/30/2017 %V 43 %N Issue 4 (Special Issue) %P 55-76 %! 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 %K Iwasawa theory‎ %K ‎automorphic representations‎ %K ‎rigid analytic geometry‎ %R %X This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $\mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2‎, ‎\mathbb{Z}_p)$‎. ‎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. %U http://bims.iranjournals.ir/article_1155_3316a1af565979a96e290f976d084d2c.pdf