Dihedral Galois representations and Katz modular forms

Reference : Dihedral Galois representations and Katz modular forms


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/11544

Title :	Dihedral Galois representations and Katz modular forms
Language :	English
Author, co-author :	Wiese, Gabor [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2004
Journal title :	Documenta Mathematica
Volume :	9
Pages :	123--133 (electronic)
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	1431-0635
Abstract :	[en] We show that any two-dimensional odd dihedral representation \rho over a finite field of characteristic p>0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of level N, character \epsilon and weight k, where N is the conductor, \epsilon is the prime-to-p part of the determinant and k is the so-called minimal weight of \rho. In particular, k=1 if and only if \rho is unramified at p. Direct arguments are used in the exceptional cases, where general results on weight and level lowering are not available.
Permalink :	http://hdl.handle.net/10993/11544

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