Zeta morphisms for rank two universal deformations

2020/06/24 by Kentaro Nakamura, Nakamura, Kentaro · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2006.13647

Abstract

In this article, we construct zeta morphisms for the universal deformations of odd absolutely irreducible two dimensional mod p Galois representations satisfying some mild assumptions, and prove that our zeta morphisms interpolate Kato's zeta morphisms for Galois representations associated to Hecke eigen cusp newforms. The existence of such morphisms was predicted by Kato's generalized Iwasawa main conjecture. Based on Kato's original construction, we construct our zeta morphisms using many deep results in the theory of p-adic (local and global) Langlands correspondence for GL_2/Q. As an application of our zeta morphisms and the resent article KLP19, we prove a theorem which roughly states that, under some mu=0 assumption, Iwasawa main conjecture without p-adic L-function for f holds if this conjecture holds for one g which is congruent to f.

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