Zeta morphisms for rank two universal deformations

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.

arXiv comment97pages (first version), 109 pages (second version). In the second version, we add an application to Iwasawa main conjecture

References in corpus (5)

• Whittaker models and the integral Bernstein center for GL_n
• Iwasawa theory of overconvergent modular forms, I: Critical $p$-adic $L$-functions
• The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in the Hecke algebra
• Le système d'Euler de Kato en famille (I)
• Iwasawa Main Conjecture for $p$-adic families of elliptic modular cuspforms

Cited by in corpus (1)

• P-adic L-functions in universal deformation families