James Arthur: “The Endoscopic Classification of Representations. Orthogonal and Symplectic Groups”

By Ulrich Görtz. Jahresbericht Der Deutschen Mathematiker-vereinigung, 2014

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Notes on Thin Matrix Groups (2012, methodology): “Namely in [Arthur 2013] a precise formulation of the Ramanujan conjectures for these groups is given, and moreover it is shown (assuming forms of the fundamental lemma which themselves should be theorems before too long) that these conjectures will follow if one can prove the Ramanujan conjectures…”
On torsion in the cohomology of locally symmetric varieties (2013, background): “As mentioned previously, these results are based on the work of Arthur, [4] (resp.”
The Gross–Prasad conjecture and local theta correspondence (2014, background): “We establish the Fourier-Jacobi case of the GP conjecture, as well as two conjectures of D. Prasad concerning local theta correspondence in the (almost) equal rank case, under the following assumptions: • We assume the local Langlands correspondence and Arthur’s multiplicity formula for unitary grou”
Rigid inner forms of real and p-adic groups (2013, methodology): “and quasi-split symplectic and orthogonal groups by Arthur [Art13].”
Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences (2012, methodology): “Now, following the Arthur multiplicity formula ([Ar12] and [Mk12]), the multiplicity in the discrete spectrum of F -quasisplit classical groups is at most one in general, except for certain cases of even special orthogonal groups where the discrete multiplicity could be two.”