Main conjectures for higher rank nearly ordinary families -- I

2017/08/15 by Kazim Büyükboduk, Büyükboduk, Kazim, Tadashi Ochiai +1 · 1 citation
Mathematics · #11F11 #11R20 #11R23 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F11 #msc:11R20 #msc:11R23

paper · pdf · doi:10.48550/arxiv.1708.04494

Many updates to earlier version. Comments most welcome!

arxiv created 2019/02/08 · arxiv updated 2019/02/11

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.

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