## Ramification of local fields with imperfect residue fields.(English)Zbl 1084.11064

Summary: 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.

### MSC:

 11S15 Ramification and extension theory 12F10 Separable extensions, Galois theory 14G22 Rigid analytic geometry
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