Descent theory in non-archimedean geometry <BR><BR>

Grothendieck's descent theory is a fundamental
tool for carrying out constructions and studying moduli spaces in
algebraic geometry. One would like to have available such a theory in
the rigid analytic setting. Because tensor products
are not algebraic but rather completed, one cannot just
copy the standard descent theory proofs. It turns out
that faithfully flat descent theory does exist in rigid analytic
geometry, but the proof that it works requires a
different approach. We explain how to do this by using Raynaud's
theory of formal models.

<BR><BR>
In the first half of the talk we will present some
background in rigid geometry and descent theory, and
in the second half we will describe the basic
ideas that go into establishing descent theory
in the non-archimedean world.