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The p-adic local langlands conjecture

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dc.contributor.advisor David A. Vogan, Jr. en_US Malon, Christopher D en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2006-07-31T15:21:48Z 2006-07-31T15:21:48Z 2005 en_US 2005 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. en_US
dc.description Includes bibliographical references (leaves 46-47). en_US
dc.description.abstract Let k be a p-adic field. Split reductive groups over k can be described up to k- isomorphism by a based root datum alone, but other groups, called rational forms of the split group, involve an action of the Galois group of k. The Galois action on the based root datum is shared by members of an inner class of k-groups, in which one k--isomorphism class is quasi-split. Other forms of the inner class can be called pure or impure, depending on the Galois action. Every form of an adjoint group is pure, but only the quasi-split forms of simply connected groups are pure. A p-adic Local Langlands correspondence would assign an L-packet, consisting of finitely many admissible representations of a p-adic group, to each Langlands parameter. To identify particular representations, data extending a Langlands parameter is needed to make "completed Langlands parameters." Data extending a Langlands parameter has been utilized by Lusztig and others to complete portions of a Langlands classification for pure forms of reductive p- adic groups, and in applications such as endoscopy and the trace formula, where an entire L-packet of representations contributes at once. en_US
dc.description.abstract (cont.) We consider a candidate for completed Langlands parameters to classify representations of arbitrary rational forms, and use it to extend a classification of certain supercuspidal representations by DeBacker and Reeder to include the impure forms. en_US
dc.description.statementofresponsibility by Christopher D. Malon. en_US
dc.format.extent 47 leaves en_US
dc.format.extent 2125656 bytes
dc.format.extent 2127516 bytes
dc.format.mimetype application/pdf
dc.format.mimetype application/pdf
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.subject Mathematics. en_US
dc.title The p-adic local langlands conjecture en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 64562675 en_US

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