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

Document Type: Special Issue of BIMS in Honor of Professor Freydoon Shahidi

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Abstract

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.

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