Reference : Modularity of certain mod p^n Galois representations
 Document type : E-prints/Working papers : Already available on another site Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/13941
 Title : Modularity of certain mod p^n Galois representations Language : English Author, co-author : Adibhatla, Rajender [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Publication date : Sep-2012 Number of pages : 10 Peer reviewed : No Keywords : [en] 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 $p^{n-1}(p-1)+1$. Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/13941 source URL : http://math.uni.lu/~adibhatla/research.html

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