Gelfand-Kirillov dimension and mod p cohomology for GL2

• 成果类型: Article
• 署名作者: Breuil, Christophe; Herzig, Florian; Hu, Yongquan; Morra, Stefano; Schraen, Benjamin
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of Toronto; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01202-8
• 发表日期: 2023
• 页码: 1-128
• 关键词: local deformation rings; modular-representations; multiplicity one; weight; conjecture; points

摘要

Let p be a prime number, F a totally real number field unramified at places above p and D a quaternion algebra of center F split at places above p and at no more than one infinite place. Let v be a fixed place of F above p and r : Gal(F/F) ? GL(2)(F-p) an irreducible modular continuous Galois representation which, at the place v, is semisimple and sufficiently generic (and satisfies some weak genericity conditions at a few other finite places). We prove that many of the admissible smooth representations of GL(2)(F-v) over F-p associated to r in the corresponding Hecke-eigenspaces of the mod p cohomology have Gelfand-Kirillov dimension [F-v : Q(p)], as well as several related results.