The canonical embedding of an unramified morphism in an étale morphism

Abstract

We show that every unramified morphism X->Y has a canonical and universal factorization X->E->Y where the first morphism is a closed embedding and the second is etale (but not separated).

18 pages (uses TikZ for figures); some minor corrections; correct proof that E_{X/Y} is locally of finite presentation (Lemma 3.2 and Appendix C); final version to appear in Math. Z

References in corpus (2)

• Submersions and effective descent of etale morphisms
• The structure of a local embedding and applications to Chern classes of weighted blow-ups

Cited by in corpus (10)

• Noetherian approximation of algebraic spaces and stacks
• Étale dévissage, descent and pushouts of stacks
• Virtual Cartier divisors and blow-ups
• The étale local structure of algebraic stacks
• Intrinsic Mirror Symmetry
• Moduli stacks of étale (phi,Gamma)-modules and the existence of crystalline lifts
• Moduli stacks of two-dimensional Galois representations
• Computing isogenies from modular equations in genus two
• A universal étale lift of a proper local embedding
• Nisnevich Descent for Deligne-Mumford Stacks