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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128066We 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.revised version, to appear in Bol. Soc. Mat. MexicanaNumber Theory11F80, 11F46Uniform behavior of families of Galois representations on Siegel modular forms and the Endoscopy Conjecturetext