Valuation theory in rigid geometry and curves over valuation rings
by
Marius van der Put
University of Antwerp

In part I, a quick informal introduction to rigid spaces will be given. Then we will present a choice out of the following examples and applications:
the Tate curve, Curves and their reductions, degenerating Abelian varieties, Raynaud's uniformization of Abelian varieties and rigid groups, the work of Raynaud and Harbater on Abhyankar's conjecture, Mumford surfaces, p-adic symmetric spaces, Drinfeld's modular curves.

In part II, the theory of sheaves and (generalized) points of rigid spaces will be introduced. This involves non trivial valuation theory for affinoid algebras. The various new spaces attached to affinoid spaces will be discussed. In the works of Huber, Berkovich, de Jong, Schneider et al, étale points, étale cohomology and étale fundamental groups were introduced and studied for the rigid situation. Some of these ideas will be explained.

Date received: July 10, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-75.