The Fontaine-Mazur conjecture in the residually reducible case
By Lue Pan. 2019
47 citations recorded by the source corpus.
We prove new cases of Fontaine-Mazur conjecture on two-dimensional Galois representations over Q when the residual representation is reducible. Our approach is via a semi-simple local-global compatibility of the completed cohomology and a Taylor-Wiles patching argument for the completed homology in this case. As a key input, we generalize the work of Skinner-Wiles in the ordinary case. In addition, we also treat the residually irreducible case at the end of the paper. Combining with people's earlier work, we can prove the Fontaine-Mazur conjecture completely in the regular case when p is at least 5.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/616e38aaf920c5913f6a0791b05c332f955ee883
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On locally analytic vectors of the completed cohomology of modular curves (2020, background): “a], Emerton formulated and proved his conjecture assuming the residual representation is irreducible and generic. Building upon the work of Paˇsku¯nas, we gave a proof (which is complete when p≥5) in [Pan19] in the case of definite quaternion algebras. We will mostly follow the argument in §3 of [Pan”