Beilinson–Bernstein Localization Over ℚ and Periods of Automorphic Forms

@article{Harris2013BeilinsonBernsteinLO,
  title={Beilinson–Bernstein Localization Over ℚ and Periods of Automorphic Forms},
  author={Michael Harris},
  journal={International Mathematics Research Notices},
  year={2013},
  volume={2013},
  pages={2000-2053}
}
  • M. Harris
  • Published 2013
  • Mathematics
  • International Mathematics Research Notices
The present paper is the first in a projected series of articles whose purpose is to draw conclusions from the comparison between an arithmetic conjecture of Deligne and an analytic conjecture of Ichino and Ikeda [D2,II]. Let F be a totally real field. The Ichino-Ikeda conjecture for unitary groups over F [II,H*] relates certain expressions in special values of automorphic L-functions with what we call GrossPrasad period integrals of automorphic representations. When these automorphic… 
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References

SHOWING 1-10 OF 39 REFERENCES
A Refined Gross-Prasad Conjecture for Unitary Groups
Let F be a number field, AF its ring of adeles, and let [pi]n and [pi]n+1 be irreducible, cuspidal, automorphic representations of SOn(AF) and SOn+1AF), respectively. In 1991, Benedict Gross and
Construction of automorphic Galois representations, II
Recent developments in the theory of the stable trace formula, especially the proof by Laumon and Ngo of the fundamental lemma for unitary groups, has revived Langlands’ strategy for constructing
Automorphic Representations, Shimura Varieties, and Motives. Ein Marchen*
1. Introduction. It had been my intention to survey the problems posed by the study of zetafunctions of Shimura varieties. But I was too sanguine. This would be a mammoth task, and limitations of
Purity Reigns Supreme
The purpose of this note is to prove the Ramanujan conjecture for cuspidal representations π of GL(n,AF ) when F is either a totally real or a CM field, and π is a cohomological representation that
Geometric Methods in Representation Theory
Introduction The goal of this series of lectures is to survey and provide background for recent joint work with Wilfried Schmid. This work has appeared as a series of papers [SV1,SV2,SV3,SV4]. The
Restrictions of representations of classical groups: examples
In an earlier paper, we considered several restriction problems in the representation theory of classical groups over local and global fields. Assuming the Langlands-Vogan parameterization of
Local-global compatibility and the action of monodromy on nearby cycles
We strengthen the local-global compatibility of Langlands correspondences for GLn in the case when n is even and l 6D p. Let L be a CM field, and let ... be a cuspidal automorphic representation of
Localization and standard modules for real semisimple Lie groups I: The duality theorem
In this paper we relate two constructions of representations of semisimple Lie groups constructions that appear quite different at first glance. Homogeneous vector bundles are one source of
Descent for Shimura varieties.
This note proves that the descent maps provided by Langlands's Con- jugacy Conjecture do satisfy the continuity condition necessary for them to be effective. Hence the conjecture does imply the
...
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