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Galois representations of orthogonal rigid local systems

URN to cite this document: urn:nbn:de:bvb:703-opus4-8485

Title data

Schulte, Michael:
Galois representations of orthogonal rigid local systems.
Bayreuth , 2012
( Doctoral thesis, 2012 , University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

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Abstract

We use the middle convolution introduced by Katz to construct a families of lisse sheaves on the affine line without two points. These correspond to continuous representations of the etale fundamental group, which can be specialized to compatible systems of Galois representations. This leads to the second maximally unipotent family. Because of the geometric origin, we can show using a theorem of Barnet-Lamb, Gee, Geraghty and Taylor that they are potentially automorphic.

Abstract in another language

Durch die von Katz eingeführte mittlere Faltung erzeugen wir glatte Garben auf der affinen Geraden ohne zwei Punkte. Diese korrespondieren zu stetigen Darstellungen der etalen Fundamentalgruppe, die zu kompatiblen Systemen von Galoisdarstellungen spezialisiert werden können. So erhalten wir die zweite maximal unipotenten Familie. Durch den geometrischen Ursprung können wir mit Hilfe eines Satzes von Barnet-Lamb, Gee, Geraghty und Taylor zeigen, dass diese potentiell automorph sind.

Further data

Item Type: Doctoral thesis (No information)
Additional notes (visible to public): msc: 11A67; msc: 12F12
Keywords: Langlands-Vermutung , Galois-Darstellung; Automorphie , Dettweiler , Katz, Taylor , Absolute Galoisgruppe; Automorphy , Dettweiler , Katz , Taylor , absolute Galois group
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-opus4-8485
Date Deposited: 25 Apr 2014 06:26
Last Modified: 25 Apr 2014 06:26
URI: https://epub.uni-bayreuth.de/id/eprint/223

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