Luis Dieulefait
Published 2003-04-27, updated 2007-04-30Version 2
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.
Comments: revised version, to appear in Bol. Soc. Mat. Mexicana
Theta operators on Siegel modular forms and Galois representations
On the images of the Galois representations attached to genus 2 Siegel modular forms
On the images of the Galois representations attached to generic automorphic representations of GSp(4)
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