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.

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.