Upper ramification groups of local fields with imperfect residue fields (1/3)
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.