Modularity of certain  2-dimensional mod p^n representations of Gal(Qbar/Q

Reference : Modularity of certain 2-dimensional mod p^n representations of Gal(Qbar/Q


	Document type :	Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/13944

Title :	Modularity of certain 2-dimensional mod p^n representations of Gal(Qbar/Q
Language :	English
Author, co-author :	Adibhatla, Rajender [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	7-Mar-2013
Audience :	International
Event name :	HIM Trimester on Arithmetic and Geometry
Event date :	7-3-2013
Event organizer :	HIM, Bonn
Event place (city) :	Bonn
Event country :	Germany
Keywords :	[en] modualr forms ; Galois representations
Abstract :	[en] For an odd rational prime p and integer n>1, we consider certain continuous representations rho_n of G_Q into GL_2(Z/p^nZ) with fixed determinant, whose local restrictions "look" like they arise from modular Galois representations, and whose mod p reductions are odd and irreducible. Under suitable hypotheses on the size of their images, we use deformation theory to lift rho_n to rho in characteristic 0. We then invoke a modularity lifting theorem of Skinner-Wiles to show that rho is modular.
Target :	Researchers ; Professionals ; Students
Permalink :	http://hdl.handle.net/10993/13944

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