The Iwasawa Main Conjectures for GL2

C Skinner, E Urban - Inventiones mathematicae, 2014 - Springer
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Iwasawa main conjecture for supersingular elliptic curves and BSD conjecture

X Wan - arXiv preprint arXiv:1411.6352, 2014 - arxiv.org
In this paper we prove the $\pm $-main conjecture of Iwasawa theory formulated by
Kobayashi for elliptic curves with supersingular reduction at an odd prime $ p $ such that …

Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields

ML Hsieh - Journal of the American Mathematical Society, 2014 - ams.org
Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields Page 1
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 27, Number 3, July 2014 …

How can we construct abelian Galois extensions of basic number fields?

B Mazur - Bulletin of the American Mathematical Society, 2011 - ams.org
Irregular primes—37 being the first such prime—have played a great role in number theory.
This article discusses Ken Ribet's construction—for all irregular primes $ p $—of specific …

-FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS

Z Liu - Journal of the Institute of Mathematics of Jussieu, 2020 - cambridge.org
We construct the p-adic standard L-functions for ordinary families of Hecke eigensystems of
the symplectic group Sp (2n)/Q using the doubling method. We explain a clear and simple …

Iwasawa–Greenberg main conjecture for nonordinary modular forms and Eisenstein congruences on GU (3, 1)

F Castella, Z Liu, X Wan - Forum of Mathematics, Sigma, 2022 - cambridge.org
In this paper, we prove one divisibility of the Iwasawa–Greenberg main conjecture for the
Rankin–Selberg product of a weight two cusp form and an ordinary complex multiplication …

Integral period relations and congruences

J Tilouine, E Urban - Algebra & Number Theory, 2022 - msp.org
Under relatively mild and natural conditions, we establish integral period relations for the
(real or imaginary) quadratic base change of an elliptic cusp form. This answers a conjecture …

Iwasawa invariants for symmetric square representations

A Ray, R Sujatha, V Vatsal - Research in the Mathematical Sciences, 2023 - Springer
Let p≥ 5 be a prime, and pa prime of Q¯ above p. Let g 1 and g 2 be p-ordinary, p-
distinguished and p-stabilized cuspidal newforms of nebentype characters ϵ 1, ϵ 2 …

Integral period relations and congruences

J Tilouine, E Urban - arXiv preprint arXiv:1811.11166, 2018 - arxiv.org
Under relatively mild and natural conditions, we establish an integral period relations for the
(real or imaginary) quadratic base change of an elliptic cusp form. This answers a conjecture …

Local Langlands correspondence, local factors, and zeta integrals in analytic families

D Disegni - Journal of the London Mathematical Society, 2020 - Wiley Online Library
We study the variation of the local Langlands correspondence for GL n in characteristic‐zero
families. We establish an existence and uniqueness theorem for a correspondence in …