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- W831027720 abstract "Three-Dimensional Galois Representations and a Conjecture of Ash, Doud and Pollack Vinh Xuan Dang Department of Mathematics Master of Science In the 1970’s and 1980’s, Jean-Pierre Serre formulated a conjecture connecting two-dimensional Galois representations and modular forms. The conjecture came to be known as Serre’s modularity conjecture. It was recently proved by Khare and Wintenberger in 2008. Serre’s conjecture has various important consequences in number theory. Most notably, it played a key role in the proof of Fermat’s last theorem. A natural question is, “what is the analogue of Serre’s conjecture for higher dimensional Galois representations?” In 2002, Ash, Doud and Pollack formulated a precise statement for a higher dimensional analogue of Serre’s conjecture. They also provided numerous computational examples as evidence for this generalized conjecture. We consider the three-dimensional version of the Ash-Doud-Pollack conjecture. We find specific examples of three-dimensional Galois representations and computationally verify the generalized conjecture in all these examples." @default.
- W831027720 created "2016-06-24" @default.
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- W831027720 date "2011-01-01" @default.
- W831027720 modified "2023-09-27" @default.
- W831027720 title "Three-Dimensional Galois Representations and a Conjecture of Ash, Doud, and Pollack" @default.
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