Ymir
Introduction
This is intended to be a Stacks Project for complex analytic spaces and nonArchimedean analytic spaces.
Ymir is a giant from Nordic mythology, who gave birth to a male and a female from his armpits. For us, Ymir contains two subclasses: a complex analytic part and a rigid analytic/Berkovich analytic part.
We will freely make use of all results from Stacks Project.
Current structure
Part 1 Preliminaries
To do: include the Archimedean theory
To do: include further details.
Part 2 Complex analytic spaces
To do: remove the Hausdorff assumptions.
To do, include Gorenstein, local complete intersection. Products.
To do, include Grauert’s direct image theorem. Include separated, proper, smooth morphisms, etc.
To do, reproduce Kiehl’s proof that the flat locus is coanalytic.
Part 3 NonArchimedean analytic spaces
To do: include Ducros’ proof of the excellence of affinoid algebras
To do: reproduce the first half of Berkovich93 PIHES. Include the theory of rigid analytic spaces.
Unwritten parts

GAGA (complex and nonArchimedean)

morphisms (Berkovich)

properties (Berkovich)

étale cohomology (Berkovich)

descent (complex and Berkovich)

differential calculus (complex)

Resolution of singularities (complex)

birational maps (complex)

vanishing theorems (complex)