5 citations · 9 across the 9 of their papers we have counts for
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Plectic Lie Algebra Action on Hilbert modular varieties
Yuanyang Jiang, Lue Pan
We construct some part of the plectic Galois action on the locally analytic -adically completed cohomology of Hilbert modular varieties, predicted by the plectic conjecture of N…
Prescribed lifts of 2-dimensional representations
Matthew Emerton, Toby Gee, Lue Pan +1
Let F be a totally real field, and let p be prime. Under standard Taylor--Wiles hypotheses, we show that an irreducible, 2-dimensional, totally odd mod p representation of the abso…
On the locally analytic completed cohomology of modular curves
Lue Pan
We survey our works on the locally analytic vectors of completed cohomology of modular curves.
Some vanishing results for the rational completed cohomology of Shimura varieties
Kai-Wen Lan, Lue Pan
Based on an almost Kodaira-type vanishing result in mixed characteristics of Bhatt, we show that, in the locally analytic completed cohomology of a general Shimura variety, suffici…
On locally analytic vectors of the completed cohomology of modular curves II
Lue Pan
This is a continuation of our previous work on the locally analytic vectors of the completed cohomology of modular curves. We construct differential operators on modular curves wit…
A note on some -adic analytic Hecke actions
Lue Pan
We show that the action of Hecke operators away from on the space of (-adic) overconvergent modular forms is (-adically) locally analytic in a certain sense. As a corolla…
On locally analytic vectors of the completed cohomology of modular curves
Lue Pan
We study the locally analytic vectors in the completed cohomology of modular curves and determine the eigenvectors of a rational Borel subalgebra of …
The Fontaine-Mazur conjecture in the residually reducible case
Lue Pan
We prove new cases of Fontaine-Mazur conjecture on two-dimensional Galois representations over Q when the residual representation is reducible. Our approach is via a semi-simple lo…
First covering of Drinfel'd upper half plane and Banach representations of GL_2(Q_p)
Lue Pan
We construct some admissible Banach representations of GL_2(Q_p) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representatio…