English

Formal models for relative adic spaces

Algebraic Geometry 2025-07-16 v1 Number Theory

Abstract

We extend Raynaud's theory of formal models from rigid-analytic spaces over a nonarchimedean field to uniform qcqs adic spaces XX, with no finite-type assumptions, over an arbitrary Tate affinoid base SS. 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.

Keywords

Cite

@article{arxiv.2507.11073,
  title  = {Formal models for relative adic spaces},
  author = {Dimitri Dine},
  journal= {arXiv preprint arXiv:2507.11073},
  year   = {2025}
}

Comments

54 pages, comments welcome!

R2 v1 2026-07-01T04:01:51.859Z