Abstract：
In general, there exist p-adic automorphic forms of different weights with the same associated p-adic Galois representation. The existence of these companion forms is also predicted by Breuil's locally analytic socle conjecture in the p-adic local Langlands program. Under the Taylor-Wiles assumption, Breuil-Hellmann-Schraen proved the existence of all companion forms when the associated crystalline Galois representations have regular Hodge-Tate weights. In this talk, I will explain how to generalize their results to some cases when the Hodge-Tate weights are not necessarily regular. The method relies on Ding's construction of partially classical eigenvarieties and their relationships with some spaces of Galois representations.
Zoom ID = 648 9548 7663
Zoom password = 525224
Zoom link = https://zoom.com.cn/j/64895487663?pwd=Q3J1WXlIaFVYSnNrUlN1b3g0ekZ2Zz09
