Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43Issue 4 (Special Issue)20170830Globally analytic $p$-adic representations of the pro--$p$--Iwahori subgroup of $GL(2)$ and base change, I : Iwasawa algebras and a base change map55761155ENL.ClozelJournal Article20170513This 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.http://bims.iranjournals.ir/article_1155_3316a1af565979a96e290f976d084d2c.pdf