Galois actions on l-adic local systems and their nearby cycles: a geometrization of fourier eigendistributions on the p-adic lie algebra sl(2)

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dc.contributor.advisorCunningham, Clifton
dc.contributor.advisorGreenberg, Matthew
dc.contributor.authorChristie, Aaron
dc.date.accessioned2017-12-18T22:37:15Z
dc.date.available2017-12-18T22:37:15Z
dc.date.issued2012
dc.descriptionBibliography: p. 101-104en
dc.description.abstractIn this thesis, two Qe-local systems, and 0 £1 (Definition 3.2.1) on the regular unipotent subvariety Uo,I< of p-adic SL(2)1< are constructed. Making use of the equiv­alence between Qe-local systems and £-adic representations of the etale fundamental group, we prove that these local systems are equivariant with respect to conjugation by SL(2)1< (Proposition 3.3.5) and that their nearby cycles, when taken with respect to appropriate integral models, descend to local systems on the regular unipotent subvariety of SL(2)k, k the residue field of K (Theorem 4.3.1). Distributions on SL(2, K) are then associated to 0 £ and 0 £1 (Definition 5.1.4) and we prove properties of these distributions. Specifically, they are admissible distributions in the sense of Harish-Chandra (Proposition 5.2.1) and, after being transferred to the Lie algebra, are linearly independent eigendistributions of the Fourier transform (Proposition 5.3.2). Together, this gives a geometrization of important admissible invariant distributions on a nonabelian p-adic group in the context of the Local Langlands program.
dc.format.extentxiii, 104 leaves : ill. ; 30 cm.en
dc.identifier.citationChristie, A. (2012). Galois actions on l-adic local systems and their nearby cycles: a geometrization of fourier eigendistributions on the p-adic lie algebra sl(2) (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/5035en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/5035
dc.identifier.urihttp://hdl.handle.net/1880/106036
dc.language.isoeng
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.titleGalois actions on l-adic local systems and their nearby cycles: a geometrization of fourier eigendistributions on the p-adic lie algebra sl(2)
dc.typedoctoral thesis
thesis.degree.disciplineMathematics and Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
ucalgary.thesis.accessionTheses Collection 58.002:Box 2104 627942974
ucalgary.thesis.notesUARCen
ucalgary.thesis.uarcreleaseyen
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