Ochiai has previously proved that the Beilinson-Kato Euler systems for
modular forms interpolate in nearly-ordinary p-adic families (Howard has
obtained a similar result for Heegner points), based on which he was able to
prove a half of the two-variable main conjectures. The principal goal of this
article is to generalize Ochiai's work in the level of Kolyvagin systems so as
to prove that Kolyvagin systems associated to Beilinson-Kato elements
interpolate in the full deformation space (in particular, beyond the
nearly-ordinary locus) and use what we call universal Kolyvagin systems to
attempt a main conjecture over the eigencurve. Along the way, we utilize these
objects in order to define a quasicoherent sheaf on the eigencurve that behaves
like a p-adic L-function (in a certain sense of the word, in
3-variables).Comment: 48 pages. Went under major revision and reorganization. Comments are
most welcome
