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Automorphic Plancherel density theorem
Let F be a totally real field, G a connected reductive group over F, and S a finite set of finite places of F. Assume that G(F ⊗ℚ ℝ) has a discrete series representation. Building upon work ofExpand
Galois representations arising from some compact Shimura varieties
Our aim is to establish some new cases of the global Langlands correspondence for GLm. Along the way we obtain a new result on the description of the cohomology of some compact Shimura varieties. LetExpand
Sato–Tate theorem for families and low-lying zeros of automorphic $$L$$L-functions
We consider certain families of automorphic representations over number fields arising from the principle of functoriality of Langlands. Let $$G$$G be a reductive group over a number field $$F$$FExpand
Patching and the p-adic local Langlands correspondence
We use the patching method of Taylor--Wiles and Kisin to construct a candidate for the p-adic local Langlands correspondence for GL_n(F), F a finite extension of Q_p. We use our construction to proveExpand
Families of L -Functions and Their Symmetry
A few years ago the first-named author proposed a working definition of a family of automorphic L-functions. Then the work by the second and third-named authors on the Sato–Tate equidistribution forExpand
Galois representations for general symplectic groups
We prove the existence of GSpin-valued Galois representations corresponding to cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields underExpand
Endoscopic Classification of Representations: Inner Forms of Unitary Groups
We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumptionExpand
On the cohomology of compact unitary group Shimura varieties at ramified split places
In this article, we prove results about the cohomology of compact unitary group Shimura varieties at split places. In nonendoscopic cases, we are able to give a full description of the cohomology,Expand