Residual irreducibility of compatible systems
We show that if {pl} is a compatible system of absolutely irreducible Galois representations of a number field then the residual representation p is absolutely irreducible for l in a density 1 set of primes. The key technical result is the following theorem: the image of pl is an open subgroup of a...
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| Format: | Journal article |
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Oxford University Press
2016
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| _version_ | 1826290168469913600 |
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| author | Patrikis, S Snowden, A Wiles, A |
| author_facet | Patrikis, S Snowden, A Wiles, A |
| author_sort | Patrikis, S |
| collection | OXFORD |
| description | We show that if {pl} is a compatible system of absolutely irreducible Galois representations of a number field then the residual representation p is absolutely irreducible for l in a density 1 set of primes. The key technical result is the following theorem: the image of pl is an open subgroup of a hyperspecial maximal compact subgroup of its Zariski closure with bounded index (as l varies). This result combines a theorem of Larsen on the semi-simple part of the image with an analogous result for the central torus that was recently proved by Barnet-Lamb, Gee, Geraghty, and Taylor, and for which we give a new proof. |
| first_indexed | 2024-03-07T02:40:04Z |
| format | Journal article |
| id | oxford-uuid:aa1ed9a6-b347-45dd-9427-eb8335fb890e |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:40:04Z |
| publishDate | 2016 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:aa1ed9a6-b347-45dd-9427-eb8335fb890e2022-03-27T03:13:07ZResidual irreducibility of compatible systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:aa1ed9a6-b347-45dd-9427-eb8335fb890eSymplectic Elements at OxfordOxford University Press2016Patrikis, SSnowden, AWiles, AWe show that if {pl} is a compatible system of absolutely irreducible Galois representations of a number field then the residual representation p is absolutely irreducible for l in a density 1 set of primes. The key technical result is the following theorem: the image of pl is an open subgroup of a hyperspecial maximal compact subgroup of its Zariski closure with bounded index (as l varies). This result combines a theorem of Larsen on the semi-simple part of the image with an analogous result for the central torus that was recently proved by Barnet-Lamb, Gee, Geraghty, and Taylor, and for which we give a new proof. |
| spellingShingle | Patrikis, S Snowden, A Wiles, A Residual irreducibility of compatible systems |
| title | Residual irreducibility of compatible systems |
| title_full | Residual irreducibility of compatible systems |
| title_fullStr | Residual irreducibility of compatible systems |
| title_full_unstemmed | Residual irreducibility of compatible systems |
| title_short | Residual irreducibility of compatible systems |
| title_sort | residual irreducibility of compatible systems |
| work_keys_str_mv | AT patrikiss residualirreducibilityofcompatiblesystems AT snowdena residualirreducibilityofcompatiblesystems AT wilesa residualirreducibilityofcompatiblesystems |