Weak local-global compatibility and ordinary representations
نویسندگان
چکیده
منابع مشابه
LOCAL - GLOBAL COMPATIBILITY FOR l
We prove the compatibility of the local and global Langlands correspondences at places dividing l for the l-adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of GLn over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing l and have Shin-regular weight. 2...
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This paper is a continuation of [HT]. Let L be an imaginary CM field and let Π be a regular algebraic (i.e., Π∞ has the same infinitesimal character as an algebraic representation of the restriction of scalars from L to Q of GLn) cuspidal automorphic representation of GLn(AL) which is conjugate self-dual (Π ◦ c ∼= Π∨) and square integrable at some finite place. In [HT] it is explained how to at...
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We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GLn over an imaginary CM or totally real field. We prove this compatibility up to semisimplification in all cases, and up to Frobenius semisimplification i...
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We study the completed cohomology Ĥ of a definite unitary group G in two variables associated with a CM-extension K/F . When the prime p splits, we prove that (under technical asumptions) the p-adic local Langlands correspondence for GL2(Qp) occurs in Ĥ. As an application, we obtain a result towards the Fontaine-Mazur conjecture over K: if x is a point on the eigenvariety such that ρx is geomet...
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We generalise Coleman’s construction of Hecke operators to define an action of GL2(Ql) on the space of finite slope overconvergent p-adic modular forms (l 6= p). In this way we associate to any Cp-valued point on the tame level N Coleman-Mazur eigencurve an admissible smooth representation of GL2(Ql) extending the classical construction. Using the Galois theoretic interpretation of the eigencur...
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ژورنال
عنوان ژورنال: Rendiconti del Seminario Matematico della Università di Padova
سال: 2018
ISSN: 0041-8994
DOI: 10.4171/rsmup/139-5