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Connecting Galois Representations with Cohomology

In this paper, we examine the conjecture of Avner Ash, Darrin Doud, David Pollack, and Warren Sinnott relating Galois representations to the mod p cohomology of congruence subgroups of the general linear group of n dimensions over the integers. We present computational evidence for this conjecture (the ADPS Conjecture) for the case n = 3 by finding Galois representations which appear to correspond to cohomology eigenclasses predicted by the ADPS Conjecture for the prime p, level N, and quadratic nebentype. The examples include representations which appear to be attached to cohomology eigenclasses which arise from D8, S3, A5, and S5 extensions. Other examples include representations which are reducible as sums of characters, representations which are symmetric squares of two-dimensional representations, and representations which arise from modular forms, as predicted by Jean-Pierre Serre for n = 2.

Identiferoai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-5123
Date23 June 2014
CreatorsAdams, Joseph Allen
PublisherBYU ScholarsArchive
Source SetsBrigham Young University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceTheses and Dissertations
Rightshttp://lib.byu.edu/about/copyright/

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