130 citations · 185 across the 19 of their papers we have counts for
22 papers
Torsion-vanishing for Siegel modular varieties via supercuspidal congruences
Ana Caraiani, Sug Woo Shin
We prove that the generic part of the cohomology of Siegel modular varieties with torsion coefficients is concentrated above the middle degree, under a suitable notion of genericit…
To be or not to be local
Christophe Breuil, Florian Herzig, Yongquan Hu +4
Let be a prime number and a finite unramified extension of . For a smooth representation of occurring in some Hecke eigenspace of the m…
Local Intertwining Relations and Co-tempered -packets of Classical Groups
Hiraku Atobe, Wee Teck Gan, Atsushi Ichino +3
The local intertwining relation is an identity that gives precise information about the action of normalized intertwining operators on parabolically induced representations. We pro…
Recent progress on Langlands reciprocity for : Shimura varieties and beyond
Ana Caraiani, Sug Woo Shin
The goal of these lecture notes is to survey progress on the global Langlands reciprocity conjecture for over number fields from the last decade and a half. We high…
The stable trace formula for Igusa varieties, II
Alexander Bertoloni Meli, Sug Woo Shin
Assuming the trace formula for Igusa varieties in characteristic p, which is known by Mack-Crane in the case of Hodge type with good reduction at p, we stabilize the formula via Ka…
The stable trace formula for Shimura varieties of abelian type
Mark Kisin, Sug Woo Shin, Yihang Zhu
We express the Frobenius-Hecke traces on the compactly supported cohomology of a Shimura variety of abelian type in terms of elliptic parts of stable Arthur-Selberg trace formulas…
of Igusa varieties via automorphic forms
Arno Kret, Sug Woo Shin
Our main theorem describes the degree 0 cohomology of Igusa varieties in terms of one-dimensional automorphic representations in the setup of mod p Hodge-type Shimura varieties wit…
Galois representations for even general special orthogonal groups
Arno Kret, Sug Woo Shin
We prove the existence of -valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of $\…
Congruences of algebraic automorphic forms and supercuspidal representations
Jessica Fintzen, Sug Woo Shin
Let be a connected reductive group over a totally real field which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p betwee…
Endoscopy and cohomology of U(n,1)
Simon Marshall, Sug Woo Shin
By assuming the endoscopic classification of automorphic representations on inner forms of unitary groups, which is currently work in progress by Kaletha, Minguez, Shin, and White,…
Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families
Ju-Lee Kim, Sug Woo Shin, Nicolas Templier
We establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes. For the tame supercuspidals…
Patching and the p-adic Langlands program for GL(2, Q_p)
Ana Caraiani, Matthew Emerton, Toby Gee +3
We present a new construction of the p-adic local Langlands correspondence for GL(2, Q_p) via the patching method of Taylor--Wiles and Kisin. This construction sheds light on the r…
Galois representations for general symplectic groups
Arno Kret, Sug Woo Shin
We prove the existence of GSpin-valued Galois representations corresponding to cohomological cuspidal automorphic representations of general symplectic groups over totally real num…
Asymptotics and local constancy of characters of p-adic groups
Ju-Lee Kim, Sug Woo Shin, Nicolas Templier
In this paper we study quantitative aspects of trace characters of reductive -adic groups when the representation varies. Our approach is based on the local constancy…
Endoscopic Classification of Representations: Inner Forms of Unitary Groups
Tasho Kaletha, Alberto Minguez, Sug Woo Shin +1
We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, und…
Families of L-functions and their Symmetry
Peter Sarnak, Sug-Woo Shin, Nicolas Templier
In [90] the first-named author gave a working definition of a family of automorphic L-functions. Since then there have been a number of works [33], [107], [67] [47], [66] and espec…
Patching and the p-adic local Langlands correspondence
Ana Caraiani, Matthew Emerton, Toby Gee +3
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 co…
Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties
Sara Arias-de-Reyna, Luis Dieulefait, Sug Woo Shin +1
This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem.…
On Fields of rationality for automorphic representations
Sug Woo Shin, Nicolas Templier
This paper proves two results on the field of rationality $\Q(π)$ for an automorphic representation , which is the subfield of $\C$ fixed under the subgroup of $\Aut(\C)$ stabil…
Sato-Tate theorem for families and low-lying zeros of automorphic -functions
Sug Woo Shin, Nicolas Templier
We consider certain families of automorphic representations over number fields arising from the principle of functoriality of Langlands. Let be a reductive group over a number…
On sparsity of positive-definite automorphic forms within a family
Junehyuk Jung
It is known due to Baker and Montgomery that almost all Fekete polynomials under certain ordering have at least one zero on the interval (0, 1). In terms of the positive-definitene…
On the cohomology of compact unitary group Shimura varieties at ramified split places
Peter Scholze, Sug Woo Shin
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…