## 抄録

Let K_{1} and K_{2} be complete discrete valuation fields of residue characteristic p > 0. Let π_{K1} and π_{K2} be their uniformizers. Let L_{1}/K_{1} and L_{2}/K _{2} be finite extensions with compatible isomorphisms of rings O{script}_{K1}/(π_{K1}^{m}) ≃ O{script} _{K2}/(π_{K2}^{m}) and O{script}L_{1}/ (π_{K1}^{m}) ≃ O{script} L_{2}/(π_{K2}^{m}) for some positive integer m which is no more than the absolute ramification indices of K_{1} and K _{2}. Let j ≤ m be a positive rational number. In this paper, we prove that the ramification of L_{1}/K_{1} is bounded by j if and only if the ramification of L_{2}/K_{2} is bounded by j. As an application, we prove that the categories of finite separable extensions of K_{1} and K_{2} whose ramifications are bounded by j are equivalent to each other, which generalizes a theorem of Deligne to the case of imperfect residue fields. We also show the compatibility of Scholl's theory of higher fields of norms with the ramification theory of Abbes-Saito, and the integrality of small Artin and Swan conductors of p-adic representations with finite local monodromy. copyright

本文言語 | 英語 |
---|---|

ページ（範囲） | 798-834 |

ページ数 | 37 |

ジャーナル | Compositio Mathematica |

巻 | 150 |

号 | 5 |

DOI | |

出版ステータス | 出版済み - 5 2014 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory