Collection Takeshi Saito - Upper ramification groups of local fields with imperfect residue fields
Upper ramification groups of local fields with imperfect residue fields were introduced by two of the organizers, Abbes and myself in 2000. Recently the graded quotients are shown to be F_p-vector spaces and related to Frobenius-Witt differentials. In three lectures, we outline the definition and recent developments. After short heuristic observation using rigid geometry leading to the definition, we will sketch:
- Definition purely in the language of schemes.
- Proof of the property that the graded quotients are F_p-vector spaces using the cotangent complexes.
- Construction of the characteristic form relating the graded quotients to Frobenius-Witt differentials. The third topic may be omitted depending on the time.
Appears in collection : Franco-Asian Summer School on Arithmetic Geometry
Organizer(s) Ahmed Abbes (CNRS & IHÉS), Ana Caraiani (Imperial College London ), Ariane Mézard (Sorbonne Université), Takeshi Saito (University of Tokyo), Takeshi Tsuji (The University of Tokyo), Daxin Xu (Chinese Academy of Sciences), Weizhe Zheng (Chinese Academy of Sciences).
Date(s) 5/30/22 - 5/31/22
linked URL https://www.ihes.fr/~abbes/Luminy/luminy2022.html