Uniform behavior of families of Galois representations on Siegel modular forms and the Endoscopy Conjecture

Details Uniform behavior of families of Galois representations on Siegel modular forms and the Endoscopy Conjecture Uniform behavior of families of Galois representations on Siegel modular forms and the Endoscopy Conjecture

2003-04-27

arxiv.org/abs/math/0304432v2

Mathematics

Number Theory

revised version, to appear in Bol. Soc. Mat. Mexicana

Scientific paper

We prove the following uniformity principle: if one of the Galois representations in the family attached to a genus two Siegel cusp form of weight $k>3$, "semistable" and with multiplicity one, is reducible (for an odd prime $p$),then all the representations in the family are reducible. This, combined with Serre's conjecture (which is now a theorem) gives a proof of the Endoscopy Conjecture.

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