Swan representations and rigid analytic curves
by
Roland Huber
Universitaet Wuppertal, Germany

By a classical construction of Artin one can attach to every finite galois extension of henselian discretely valued fields of rank 1 with algebraically closed residue fields a finite dimensional representation of the galois group. One can extend this construction to a more general class of valued fields. These valued fields and their associated Artin representations occur in rigid analytic geometry. They have applications in the etale cohomology of rigid analytic curves. For example, one obtains a Grothendieck-Ogg-Shafarevich formula for constructible etale sheaves.

Date received: March 2, 1999