Hensel-lifting torsion points on Jacobians and Galois representations
| Autor: | Nicolas Mascot |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics::Number Theory Applied Mathematics 010103 numerical & computational mathematics Galois module 01 natural sciences 010101 applied mathematics Computational Mathematics symbols.namesake Jacobian matrix and determinant symbols Torsion (algebra) 0101 mathematics Mathematics Characteristic polynomial |
| Zdroj: | Mathematics of Computation. 89:1417-1455 |
| ISSN: | 1088-6842 0025-5718 |
| DOI: | 10.1090/mcom/3484 |
| Popis: | Let $\rho$ be a mod $\ell$ Galois representation. We show how to compute $\rho$, given the characteristic polynomial of the image of the Frobenius at one prime $p$ and a curve $C$ whose Jacobian contains $\rho$ in its $\ell$-torsion. The main ingredient is a method to $p$-adically lift torsion points on a Jacobian in the framework of Makdisi's algorithms. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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