43 citations · 202 across the 24 of their papers we have counts for
25 papers
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…
On vector-valued twisted conjugate invariant functions on a group
Liang Xiao, Xinwen Zhu
We study the space of vector-valued (twisted) conjugate invariant functions on a connected reductive group.
Cycles on Shimura varieties via geometric Satake
Liang Xiao, Xinwen Zhu
We construct (cohomological) correspondences between mod fibers of different Shimura varieties and describe the fibers of these correspondences by studying irreducible componen…