Kottwitz's nearby cycles conjecture for a class of unitary Shimura varieties

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dc.contributor.advisorHaines, Thomasen_US
dc.contributor.authorRostami, Seanen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2012-07-14T05:32:54Z
dc.date.available2012-07-14T05:32:54Z
dc.date.issued2011en_US
dc.description.abstractThis paper proves that the nearby cycles complex on a certain family of PEL local models is central with respect to the convolution product of sheaves on the corresponding affine flag variety. As a corollary, the semisimple trace function defined using the action of Frobenius on that nearby cycles complex is, via the sheaf-function dictionary, in the center of the corresponding Iwahori-Hecke algebra. This is commonly referred to as Kottwitz's conjecture. The reductive groups associated to the PEL local models under consideration are unramified unitary similitude groups with even dimension. The proof follows the method of [Haines-Ngo 2002].en_US
dc.identifier.urihttp://hdl.handle.net/1903/12853
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledbernstein basis functionen_US
dc.subject.pquncontrolledkottwitz conjectureen_US
dc.subject.pquncontrolledlocal modelsen_US
dc.subject.pquncontrollednearby cyclesen_US
dc.subject.pquncontrolledshimura varietiesen_US
dc.subject.pquncontrolledunitary groupen_US
dc.titleKottwitz's nearby cycles conjecture for a class of unitary Shimura varietiesen_US
dc.typeDissertationen_US

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