A $p$ -adic nonabelian criterion for good reduction of curves
Let K be a complete discrete valuation field of characteristic 0, with valuation ring OK and perfect residue field k of positive characteristic p. We prove that a proper and smooth curve over K, admitting a semistable model over OK, has good reduction if and only if its unipotent p-adic étale fundam...
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| Format: | Journal article |
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Duke University Press
2015
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| _version_ | 1826281050591985664 |
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| author | Andreatta, F Iovita, A Kim, M |
| author_facet | Andreatta, F Iovita, A Kim, M |
| author_sort | Andreatta, F |
| collection | OXFORD |
| description | Let K be a complete discrete valuation field of characteristic 0, with valuation ring OK and perfect residue field k of positive characteristic p. We prove that a proper and smooth curve over K, admitting a semistable model over OK, has good reduction if and only if its unipotent p-adic étale fundamental group is crystalline. |
| first_indexed | 2024-03-07T00:22:57Z |
| format | Journal article |
| id | oxford-uuid:7d2bc19f-dd30-4a4e-b39e-57bd35de0404 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:22:57Z |
| publishDate | 2015 |
| publisher | Duke University Press |
| record_format | dspace |
| spelling | oxford-uuid:7d2bc19f-dd30-4a4e-b39e-57bd35de04042022-03-26T21:01:45ZA $p$ -adic nonabelian criterion for good reduction of curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7d2bc19f-dd30-4a4e-b39e-57bd35de0404Symplectic Elements at OxfordDuke University Press2015Andreatta, FIovita, AKim, MLet K be a complete discrete valuation field of characteristic 0, with valuation ring OK and perfect residue field k of positive characteristic p. We prove that a proper and smooth curve over K, admitting a semistable model over OK, has good reduction if and only if its unipotent p-adic étale fundamental group is crystalline. |
| spellingShingle | Andreatta, F Iovita, A Kim, M A $p$ -adic nonabelian criterion for good reduction of curves |
| title | A $p$ -adic nonabelian criterion for good reduction of curves |
| title_full | A $p$ -adic nonabelian criterion for good reduction of curves |
| title_fullStr | A $p$ -adic nonabelian criterion for good reduction of curves |
| title_full_unstemmed | A $p$ -adic nonabelian criterion for good reduction of curves |
| title_short | A $p$ -adic nonabelian criterion for good reduction of curves |
| title_sort | p adic nonabelian criterion for good reduction of curves |
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