On refined ramification filtrations in the equal characteristic case

Details On refined ramification filtrations in the equal characteristic case On refined ramification filtrations in the equal characteristic case

2009-11-09

arxiv.org/abs/0911.1802v3

Mathematics

Number Theory

typos and errors corrected; mostly improvement on English and presentation

Scientific paper

Let k be a complete discrete valuation field of equal characteristic p>0. Using the tools of p-adic differential modules, we define refined Artin and Swan conductors for a representation of the absolute Galois group $G_k$ with finite local monodromy; this leads to a description of the subquotients of the ramification filtration on $G_k$. We prove that our definition of the refined Swan conductors coincide with that is given by Saito, which uses etale cohomology. We also study its relation with the toroidal variation of the Swan conductors.

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