FINDING GALOIS REPRESENTATIONS CORRESPONDING TO CERTAIN HECKE EIGENCLASSES
| Autor: | Meghan Dewitt, Darrin Doud |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics - Number Theory Galois cohomology Mathematics::Number Theory Fundamental theorem of Galois theory Galois group Galois module 11F80 11F75 Embedding problem Algebra Differential Galois theory Normal basis symbols.namesake FOS: Mathematics symbols Number Theory (math.NT) Galois extension Mathematics |
| Zdroj: | International Journal of Number Theory. :1-11 |
| ISSN: | 1793-7310 1793-0421 |
| Popis: | In 1992, Ash and McConnell presented computational evidence of a connection between three-dimensional Galois representations and certain arithmetic cohomology classes. For some examples, they were unable to determine the attached representation. For several Hecke eigenclasses (including one for which Ash and McConnell did not find the Galois representation), we find a Galois representation which appears to be attached and show strong evidence for the uniqueness of this representation. The techniques that we use to find defining polynomials for the Galois representations include a targeted Hunter search, class field theory and elliptic curves. |
| Databáze: | OpenAIRE |
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