Strong local-global compatibility in the p-adic Langlands program for U(2)
نویسندگان
چکیده
For certain mod p Galois representations ρ̄, arising from modular forms on definite unitary groups in two variables, we express the ρ̄-part of completed cohomology Ĥ ρ̄ (away from Σ = Σp ∪Σ0) as a tensor product Πp⊗ΠΣ0 . Here Πp is attached to the universal deformation ρ via the p-adic local Langlands correspondence for GL2(Qp), and ΠΣ0 is given by the local Langlands correspondence in families, of Emerton and Helm. 1 2
منابع مشابه
Weak local-global compatibility in the p-adic Langlands program for U(2)
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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