43 citations · 202 across the 24 of their papers we have counts for
21 papers · 1 filter
Slopes of modular forms and geometry of eigencurves
Ruochuan Liu, Nha Xuan Truong, Liang Xiao +1
Under a stronger genericity condition, we prove the local analogue of ghost conjecture of Bergdall and Pollack. As applications, we deduce in this case (a) a folklore conjecture of…
A local analogue of the ghost conjecture of Bergdall-Pollack
Ruochuan Liu, Nha Xuan Truong, Liang Xiao +1
We formulate a local analogue of the ghost conjecture of Bergdall and Pollack, which essentially relies purely on the representation theory of GL_2(Q_p). We further study the combi…
Deformation of rigid conjugate self-dual Galois representations
Yifeng Liu, Yichao Tian, Liang Xiao +2
In this article, we study deformations of conjugate self-dual Galois representations. The study has two folds. First, we prove an R=T type theorem for a conjugate self-dual Galois…
On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives
Yifeng Liu, Yichao Tian, Liang Xiao +2
In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the…
Slopes for higher rank Artin-Schreier-Witt Towers
Rufei Ren, Daqing Wan, Liang Xiao +1
We fix a monic polynomial over a finite field of characteristic , and consider the -Artin-Schreier-Witt tower defined by $…
The eigencurve over the boundary of weight space
Ruochuan Liu, Daqing Wan, Liang Xiao
We prove that the eigencurve associated to a definite quaternion algebra over $\QQ$ satisfies the following properties, as conjectured by Coleman--Mazur and Buzzard--Kilford: (a) o…