Modularity of certain mod $p^n$ Galois representations
| Autor: | Adibhatla, Rajender |
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| Rok vydání: | 2013 |
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| Druh dokumentu: | Working Paper |
| Popis: | For a rational prime $p \geq 3$ and an integer $n \geq 2$, we study the modularity of continuous 2-dimensional mod $p^n$ Galois representations of $\Gal(\bar{\Q}/\Q)$ whose residual representations are odd and absolutely irreducible. Under suitable hypotheses on the local structure of these representations and the size of their images we use deformation theory to construct characteristic 0 lifts. We then invoke modularity lifting results to prove that these lifts are modular. As an application, we show that certain unramified mod $p^n$ Galois representations arise from modular forms of weight $p^{n-1}(p-1)+1$. Comment: 10 pages. Minor structural changes from previous version. arXiv admin note: substantial text overlap with arXiv:1007.0181 |
| Databáze: | arXiv |
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