Ramification of local fields with imperfect residue fields

By Ahmed Abbes, Takeshi Saito. 2000

153 citations recorded by the source corpus.

We define two decreasing filtrations by ramification groups on the absolute Galois group of a complete discrete valuation field whose residue field may not be perfect. In the classical case where the residue field is perfect, we recover the classical upper numbering filtration. The definition uses rigid geometry and log-structures. We also establish some of their properties.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2df91e0b3b05dca551d47cf25e0c4e42b4233c70

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In Computational Theory and Mathematics

1. Ruochuan Liu
2. Laurent Fargues
3. Y. Andr'e
4. Takeshi Saito
5. Kiran S. Kedlaya
6. Alan G. B. Lauder
7. T. Mochizuki
8. Davesh Maulik

In Geometry and Topology

1. Kiran S. Kedlaya
2. Ruochuan Liu
3. Laurent Fargues
4. Y. Andr'e
5. Takeshi Saito
6. Peter Scholze
7. Jonathan Pottharst
8. T. Mochizuki

In Mathematical Physics

1. Kiran S. Kedlaya
2. Ruochuan Liu
3. Laurent Fargues
4. Y. Andr'e
5. Peter Scholze
6. Takeshi Saito
7. Jonathan Pottharst
8. Kentaro Nakamura

Citations in the corpus

• La filtration canonique des points de torsion des groupes $p$-divisibles (2011, background): “T, An upper bound on the Abbes-Saito filtration for finite flat group schemes and applications, prépublication arXiv:1004.4205.”
• Relative p-adic Hodge theory, II: Imperfect period rings (2016, background): “Namely, it seems to require a deep understanding of higher ramification theory, perhaps in the form developed by Abbes and Saito [2, 3], in order to feed into the machinery of relative (φ,Γ)-modules proposed by Scholl [94].”
• The characteristic cycle and the singular support of a constructible sheaf (2015, methodology): “21) is reduced to the case where F = j!G[1] for the open immersion j : U = X Z → X and a locally constant sheaf G on U .”
• Filtrations de type Hasse-Arf et monodromie p-adique (2002, background): “récemment, Abbes et Saito ont défini une filtration par les p ntes surRepE(GK) sans l’hypothèse quek soit parfait [1], mais il n’est pas clair que ce soit une filtra tion de Hasse-Arf.”
• La filtration de Harder-Narasimhan des schémas en groupes finis et plats (2010, background): “Références [1] Ahmed Abbes and Takeshi Saito.”
• Wild ramification and the characteristic cycle of an ℓ-adic sheaf (2007, methodology): “The theory of logarithmic ramification groups of a local field with imperfect residue field as developed in [1] and [2] relies on rigid geometry and on log geometry in an essential way.”
• Slope filtrations (2008, background): “[14] L. Barbieri-Viale, A. Rosenschon, M. Saito, Deligne’sconjecture on1-motives, Ann. of Math.”