Formal models for relative adic spaces

Abstract

We extend Raynaud's theory of formal models from rigid-analytic spaces over a nonarchimedean field to uniform qcqs adic spaces $X$, with no finite-type assumptions, over an arbitrary Tate affinoid base $S$. The key new ingredient is the notion of a normalized formal blow-up which takes on the role played by admissible formal blow-ups in the classical theory.

arXiv commentMajor revision. Main theorem now uses compositions of normalized formal blow-ups. Added Proposition 6.2, Proposition 6.3, Lemma 6.5, Lemma 6.7. Removed Proposition 6.7 of the previous version. 56 pages