摘要
In the p-adic local Langlands correspondence for GL2(Qp),the following theorem of Berger and Breuil has played an important role:the locally algebraic representations of GL2(Qp)associated to crystabelline Galois representations admit a unique unitary completion.In this note,we give a new proof of the weaker statement that the locally algebraic representations admit at most one unitary completion and such a completion is automatically admissible.Our proof is purely representation theoretic,involving neither(ψ,Γ)-module techniques nor global methods.When F is a finite extension of Qp,we also get a simpler proof of a theorem of Vignéras for the existence of integral structures for(locally algebraic)special series and for(smooth)tamely ramified principal series.
基金
National Natural Science Foundation of China(Grant No.11688101)
China’s Recruitement Program of Global Experts
National Center for Mathematics and Interdisciplinary Sciences
Hua Loo-Keng Center for Mathematical Sciences of Chinese Academy of Sciences。
