Representations of p-adic groups Theorems and notes
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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
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 distribut...
متن کاملCMI SUMMER SCHOOL NOTES ON p - ADIC HODGE THEORY ( PRELIMINARY VERSION )
Part I. First steps in p-adic Hodge theory 4 1. Motivation 4 1.1. Tate modules 4 1.2. Galois lattices and Galois deformations 6 1.3. Aims of p-adic Hodge theory 7 1.4. Exercises 9 2. Hodge–Tate representations 10 2.1. Basic properties of CK 11 2.2. Theorems of Tate–Sen and Faltings 12 2.3. Hodge–Tate decomposition 15 2.4. Formalism of Hodge–Tate representations 17 2.5. Exercises 24 3. Étale φ-m...
متن کاملRepresentations of Reductive Groups
This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Qp and Fq((s))]. In this part I’ll closely follow the notes of the course of J.Bernstein. Moreover I’ll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Qp((s))]. In th...
متن کاملFiltrations of smooth principal series and Iwasawa modules
Let $G$ be a reductive $p$-adic group. We consider the general question of whether the reducibility of an induced representation can be detected in a ``co-rank one" situation. For smooth complex representations induced from supercuspidal representations, we show that a sufficient condition is the existence of a subquotient that does not appear as a subrepresentation. An import...
متن کاملSome bounds on unitary duals of classical groups - non-archimeden case
We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups. Roughly, they can show up only if the central character of the inducing irreducible cuspidal representation is dominated by the square root of the modular character of the minimal parabolic subgroup. For unitarizable subquotients...
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