Blowing up in Rigid Analytic Geometry
نویسنده
چکیده
We define the concept of blowing up map in rigid analytic geometry and show that such maps exist in full generality by giving an explicit construction. We then derive some elementary properties of blowing up maps, similar to those in the classical case. 0 Introduction and preliminaries 0.
منابع مشابه
Rigid Analytic Flatificators
Let K be an algebraically closed field endowed with a complete non-archimedean norm. Let f : Y → X be a map of K-affinoid varieties. We prove that for each point x ∈ X, either f is flat at x, or there exists, at least locally around x, a maximal locally closed analytic subvariety Z ⊂ X containing x, such that the base change f−1(Z)→ Z is flat at x, and, moreover, g−1(Z) has again this property ...
متن کاملAn Introduction to Rigid Analytic Geometry
These notes are intended to be a short course in rigid analytic geometry, without, however, providing always proofs. The excellent book [4] by Bosch, Güntzer and Remmert is an extensive introduction into rigid analytic geometry, and includes all the proofs I have omitted here.
متن کاملFlattening and Subanalytic Sets in Rigid Analytic Geometry
Let K be an algebraically closed field endowed with a complete nonarchimedean norm with valuation ring R. Let f : Y → X be a map of K-affinoid varieties. In this paper we study the analytic structure of the image f(Y ) ⊂ X; such an image is a typical example of a subanalytic set. We show that the subanalytic sets are precisely the D-semianalytic sets, where D is the truncated division function ...
متن کاملEtale Cohomology of Rigid Analytic Spaces
The paper serves as an introduction to etale cohomology of rigid analytic spaces. A number of basic results are proved, e.g. concerning cohomological dimension, base change, invariance for change of base elds, the homotopy axiom and comparison for etale cohomology of algebraic varieties. The methods are those of classical rigid analytic geometry and along the way a number of known results on ri...
متن کاملRigid-analytic geometry and the uniformization of abelian varieties
The purpose of these notes is to introduce some basic notions of rigid-analytic geometry, with the aim of discussing the non-archimedean uniformizations of certain abelian varieties.
متن کامل