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Automorphic Plancherel density theorem

- S. Shin
- Mathematics
- 28 February 2012

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 of… Expand

Galois representations arising from some compact Shimura varieties

- S. Shin
- Mathematics
- 1 May 2011

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. Let… Expand

Sato–Tate theorem for families and low-lying zeros of automorphic $$L$$L-functions

- S. Shin, Nicolas Templier
- Mathematics
- 9 August 2012

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 $$F$$F… Expand

Patching and the p-adic local Langlands correspondence

- A. Caraiani, M. Emerton, T. Gee, D. Geraghty, Vytautas Paškūnas, S. Shin
- Mathematics
- 2 October 2013

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 prove… Expand

Families of L -Functions and Their Symmetry

- P. Sarnak, S. Shin, Nicolas Templier
- Mathematics
- 21 January 2014

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 for… Expand

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 under… Expand

Endoscopic Classification of Representations: Inner Forms of Unitary Groups

- Tasho Kaletha, A. M'inguez, S. Shin, P. White
- Mathematics
- 12 September 2014

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 assumption… Expand

Families of Automorphic Forms and the Trace Formula

- W. Müller, S. Shin, Nicolas Templier
- Mathematics
- 2016

On the cohomology of compact unitary group Shimura varieties at ramified split places

- P. Scholze, S. Shin
- Mathematics
- 2 October 2011

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

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