Abstract
Serre's conjecture on the modularity of Galois representations makes a connection between two-dimensional Galois representations and modular forms. A conjecture by Ash, Doud, and Pollack generalizes Serre's to higher-dimensional Galois representations. In this paper we discuss an explicit computational example supporting the generalized claim. An ambiguity in a calculation within the example is resolved using a method of complex approximation.
Degree
MS
College and Department
Physical and Mathematical Sciences; Mathematics
Rights
http://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Hansen, Brian Francis, "Explicit Computations Supporting a Generalization of Serre's Conjecture" (2005). Theses and Dissertations. 323.
https://scholarsarchive.byu.edu/etd/323
Date Submitted
2005-06-03
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd842
Keywords
Serre, conjecture, Galois representations, modular forms, complex approximation, Ash, Doud, Pollack, computation
Language
English