THE FONTAINE-MAZUR CONJECTURE IN THE RESIDUALLY REDUCIBLE CASE

Lue Pan

doi:10.1090/jams/991

THE FONTAINE-MAZUR CONJECTURE IN THE RESIDUALLY REDUCIBLE CASE

Lue Pan

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	1031-1169
Number of pages	139
Journal	Journal of the American Mathematical Society
Volume	35
Issue number	4
DOIs	https://doi.org/10.1090/jams/991
State	Published - 2022

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/jams/991

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title = "THE FONTAINE-MAZUR CONJECTURE IN THE RESIDUALLY REDUCIBLE CASE",

abstract = "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.",

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AB - 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.

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THE FONTAINE-MAZUR CONJECTURE IN THE RESIDUALLY REDUCIBLE CASE

Abstract

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