WorkshopsA remark on the cohomology of some unitary Shimura varieties
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There is a conjectural counting point formula for the special fibers of Shimura varieties (with no level structure at p), which has been established for PEL Shimura varieties of unitary or symplectic type. (There are partial results in some other cases.) I will explain a technique (in progress) which will eventually enable us to identify the Eisenstein part in the alternating sum of the compact support cohomology (or the usual cohomology) starting from the counting point formula. As we usually don't know yet enough about the automorphic representations of the relevant group, the results would often be partial or conditional.
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Sug Woo Shin
2010-07-16
09:00:00 - 10:20:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
There is a conjectural counting point formula for the special fibers of Shimura varieties (with no level structure at p), which has been established for PEL Shimura varieties of unitary or symplectic type. (There are partial results in some other cases.) I will explain a technique (in progress) which will eventually enable us to identify the Eisenstein part in the alternating sum of the compact support cohomology (or the usual cohomology) starting from the counting point formula. As we usually don't know yet enough about the automorphic representations of the relevant group, the results would often be partial or conditional.