Global rigid inner forms and multiplicities of discrete automorphic representations

Bounds for the multiplicities of cohomological automorphic forms on GL2

We prove a power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL2 over any number field that is not totally real. Our proof involves the theory of p-adically completed cohomology developed by Calegari and Emerton and a bound for the growth of coinvariants in certain finitely generated noncommutative Iwasawa modules.

Week 1: Automorphic Forms and Representations

Brief introduction to cyclotomic theory over Q using adeles. Discussion of the definitions of modular forms and automorphic forms. Introducing the adelic automorphic forms via strong approximation theorem. Discussion of the connected components of Shimura varieties (modular curves). Smooth/admissible representations of locally finite groups. Definition and admissibility of (cuspidal) automorphi...

Automorphic forms and - adic representations 4

In Carayol’s note [4], a geometric construction of the Galois representations associated to Hilbert modular forms and the compatibility with the local Langlands correspondence are discussed. In loc. cit., the compatibility is established in the case = p where the Galois representation is an -adic representation and p is the prime divided by the prime p of the totally real field where the restri...

Galois Representations and Automorphic Forms (MasterMath)

Unipotent Automorphic Representations : Global Motivation

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