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Title: The Fontaine-Mazur conjecture in the residually reducible case
Authors: Pan, Lue
Advisors: Taylor, Richard L
Contributors: Mathematics Department
Keywords: completed cohomology
Fontaine-Mazur conjecture
Galois representation
p-adic local Langlands
Subjects: Mathematics
Issue Date: 2018
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis, 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 also generalize works of Skinner-Wiles in the ordinary case.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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