43 citations · 202 across the 24 of their papers we have counts for
7 papers · 1 filter
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…
Unramifiedness of Galois representations arising from Hilbert modular surfaces
Matthew Emerton, Davide A. Reduzzi, Liang Xiao
Let be a prime number and a totally real number field. For each prime of above we construct a Hecke operator acting on $(\mathrm{mod…
On the parity conjecture in finite-slope families
Jonathan Pottharst, Liang Xiao
We generalize to the finite-slope setting several techniques due to Nekovar concerning the parity conjecture for self-dual motives. In particular we show that, for a -adic analy…
On Tate conjecture for the special fibers of some unitary Shimura varieties
David Helm, Yichao Tian, Liang Xiao
Let be a totally real field in which a fixed prime is inert, and let be a CM extension of in which splits. We fix two positive integers . We…
Tate cycles on some quaternionic Shimura varieties mod p
Yichao Tian, Liang Xiao
Let be a totally real field in which a prime number is inert. We continue the study of the (generalized) Goren--Oort strata on quaternionic Shimura varieties over finite…
Slopes of eigencurves over boundary disks
Daqing Wan, Liang Xiao, Jun Zhang
Let be a prime number. We study the slopes of -eigenvalues on the subspace of modular forms that can be transferred to a definite quaternion algebra. We give a sharp lower…