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Title: Shimura varieties for unitary groups and the doubling method
ThetheoryofGaloisrepresentationsattachedtoautomorphicrepresenta- tions of GL(n) is largely based on the study of the cohomology of Shimura varieties of PEL type attached to unitary similitude groups. The need to keep track of the similitude factor complicates notation while making no difference to the final result. It is more natural to work with Shimura varieties attached to the unitary groups themselves, which do not introduce these unnecessary complications; however, these are of abelian type, not of PEL type, and the Galois representations on their cohomology differ slightly from those obtained from the more familiar Shimura varieties. Results on the critical values of the L-functions of these Galois representations have been established by studying the PEL type Shimura varieties. It is not immediately obvious that the automorphic periods for these varieties are the same as for those attached to unitary groups, which appear more naturally in applications of relative trace formulas, such as the refined Gan-Gross-Prasad conjecture (conjecture of Ichino-Ikeda and N. Harris). The present article reconsiders these critical values, using the Shimura varieties attached to unitary groups, and obtains results that can be used more simply in applications.  more » « less
Award ID(s):
2001369
PAR ID:
10320702
Author(s) / Creator(s):
Editor(s):
Müller, Werner; Shin, Sug Woo; Templier, Nicolas
Date Published:
Journal Name:
Relative Trace Formulas
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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