A Note on Integral Structures in Some Locally Algebraic Representations of GL2

• 作者: Yong Quan HU
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 59-72
• 页数: 14页
• 语种: 英文

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 (?,Γ)-module techniques nor global methods. When F is a finite extension of Qp, we also get a simpler proof of a theorem of Vign′eras for the existence of integral structures for (locally algebraic) special series and for (smooth) tamely ramified principal series.