Download A user's guide to the trace formula for covering groups - Wen

Non-invariant trace formula
The refined geometric side
One difficulty
Arthur’s proof can be adapted to prove the refined geometric expansion.
But it requires new ideas as well.
In the course of proof, one has to show that aM̃ (S, γḟ
ḟ
S )JM̃S (γ
S, f)
behaves well with respect to the correspondence γ ⇝ γf
.
S
Unlike the case treated by Arthur, the character [·, σ] intervenes and
we need a somewhat technical result of “transport of structure” for
aM̃ (S, γḟ
ḟ
S ) and JM̃S (γ
S , f ).
Wen-Wei Li
Trace formula for covers
July 24, 2012
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