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Modularity of certain mod p^n Galois representations
Adibhatla, Rajender
2012
 

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Keywords :
modular forms; Galois representations; deformation theory of Galois representations
Abstract :
[en] 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 $\Gal(\overline{\Q}/\Q)$ 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 $p^{n-1}(p-1)+1$.
Disciplines :
Mathematics
Author, co-author :
Adibhatla, Rajender ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Modularity of certain mod p^n Galois representations
Publication date :
September 2012
Number of pages :
10
Available on ORBilu :
since 31 December 2013

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