Zeta Morphisms for Rank Two Universal Deformations
Shimura Varieties and LFunctions March 13, 2023  March 17, 2023
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Kato’s Euler system
padic Langlands correpondence
completed cohomology
In his work on the Iwasawa main conjecture for elliptic Hecke eigen cusp newforms, Kazuya Kato constructed a map which we call the zeta morphism whose target is the Iwasawa cohomology of the associated padic Galois representations. Combining FukayaKato’s idea for constructing the zeta morphisms for Hida families with many deep results in the padic (local and global) Langlands correspondence for GL_2/Q, we extend this map for the universal deformations of odd absolutely irreducible mod p Galois representations of rank two. As an application, we prove a theorem, which roughly says that, under some mu= 0 assumption, the Iwasawa main conjecture (without padic L function) for one modular form implies the same conjecture for arbitrary congruent modular forms.
Kentaro Nakamura

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Kentaro Nakamura

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