Arthur's conjectures is a noted mathematical theorem paper written in 1989 by James Arthur. Arthur is the former president of the American Mathematical Society and a Professor at the University of Toronto. His conjectures deal with Unipotent Automorphic Representations on local and global scales. Test your knowledge with this quiz!
Make sense of semisimple and unipotent representations of automorphic forms.
Describe how conjectures relate to the spectral side of the trace formula.
Show the functorial lifting of a reductive group.
Prove Z(H) is the center of group H.
Dealing only with local conjectures.
Dealing only with global conjectures.
A subgroup where all elements remain unchanged in value when operated on by themselves.
A subgroup having only one element that is unchanged in value when operated on by itself.
Individuals, Group
Packets, Individual
Groups, Parabolic
Parabolas, Packet
Derivative Formula
Trace Formula
Inverse Function Formula
Law of Sines Formula
Langlands worked with functorial lifting of unitary characters. Arthur worked with lifting of a reductive group
Langlands proved functoriality for non-Archimedean fields. Arthur worked on Archimedean fields
Langlands worked with functorial lifting of a reductive group. Arthur worked with lifting of unitary characters
Langlands and Arthur's work have no differences because they always worked together
Parabolic algebraic group of points centering on a line
Linear algebraic group over a field
Clustered algebraic group over a field
Geometric points forming a line over a field
Langlands and Shelstad
Langlands and Bell
Arthur and Shelstad
Friberg and Grioux
Endoscopy hasn't been proven with tempered representations and he had a hypothesis on how to do so
In order to understand linear groups better he needed to use elements of endoscopy
He wanted to apply his theory to non-tempered representations, where he needed to consider endoscopic groups.
He worked with endoscopic groups to create reductive groups
Algebraic and linear
Combinatorial, representation-theoretic and arguably geometric
Automorphic-representative and geometric
Functoriality
Cannot calculate the twisted characters
The ellipse cannot be complete
The parameters cannot be cuspidal
The parameters cannot be linear