We define generalizations of classical invariants of wild ramification for
coverings on a variety of arbitrary dimension over a local field. For an l-adic
sheaf, we define its Swan class as a 0-cycle class supported on the wild
ramification locus. We prove a formula of Riemann-Roch type for the Swan
conductor of cohomology together with its relative version, assuming that the
local field is of mixed characteristic.
We also prove the integrality of the Swan class for curves over a local field
as a generalization of the Hasse-Arf theorem. We derive a proof of a conjecture
of Serre on the Artin character for a group action with an isolated fixed point
on a regular local ring, assuming the dimension is 2.Comment: 159 pages, some corrections are mad
