30 citations · 110 across the 16 of their papers we have counts for
16 papers
Kato's main conjecture for nonordinary modular forms
Francesc Castella, Zheng Liu, Xin Wan
We prove Kato's main conjecture for modular forms at nonordinary primes for weights in the Fontaine-Laffaille range. The key ingredients in the proof are a reformulation of the con…
-adic Waldspurger Formula for Non-split Primes and Converse of Gross--Zagier and Kolyvagin Theorem
Yangyu Fan, Xin Wan
Let be a prime and be an imaginary quadratic field. In this paper we generalize a recent construction of a new type of -adic -function and -adic Waldspur…
Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on
Francesc Castella, Zheng Liu, Xin Wan
In this paper we prove one side divisibility of the Iwasawa-Greenberg main conjecture for Rankin-Selberg product of a weight two cusp form and an ordinary CM form of higher weight,…
The Iwasawa Main Conjecture for universal families of modular motives
Olivier Fouquet, Xin Wan
Let be an odd prime. We prove the cyclotomic Iwasawa Main Conjecture of K.Kato for the motive attached to an eigencuspform with arbitrary reduction type…
The Iwasawa Main Conjectures for and derivatives of -adic -functions
Francesc Castella, Xin Wan
We prove under mild hypotheses the three-variable Iwasawa main conjecture for -ordinary modular forms in the indefinite setting. Our result is in a setting complementary to that…
Iwasawa theory for , Bloch-Kato conjecture and Functional Equation
Xin Wan
In this paper we develop a new method to study Iwasawa theory and Eisenstein families for unitary groups of general signature over a totally real field . As a…