Main conjectures for higher rank nearly ordinary families -- I

Abstract

In this article, we present the first half of our project on the Iwasawa theory of higher rank Galois deformations over deformations rings of arbitrary dimension. We develop a theory of Coleman maps for a very general class of coefficient rings, devise a dimension reduction procedure for locally restricted Euler systems and finally, put these into use in order to prove a divisibility in a 3-variable main conjecture for nearly ordinary families of Rankin-Selberg convolutions.

Many updates to earlier version. Comments most welcome!

References in corpus (4)

• Rankin--Eisenstein classes and explicit reciprocity laws
• Images of adelic Galois representations for modular forms
• On the Brauer class of Modular Endomorphism Algebras
• $p$-adic heights of Heegner points and Beilinson-Flach elements

Cited by in corpus (1)

• Codimension two cycles in Iwasawa theory and tensor product of Hida families