A proof of the Breuil-Schneider conjecture in the indecomposable case

• 成果类型: Article
• 署名作者: Sorensen, Claus M.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.177.1.7
• 发表日期: 2013
• 页码: 367-382
• 关键词: representations; invariant; EXISTENCE

摘要

This paper contains a proof of a conjecture of Breuil and Schneider, on the existence of an invariant norm on any locally algebraic representation of GL(n), with integral central character, whose smooth part is given by a generalized Steinberg representation. In fact, we prove the analogue for any connected reductive group G. This is done by passing to a global setting, using the trace formula for an R-anisotropic model of G. The ultimate norm comes from classical p-adic modular forms.