nLab etale morphisms - contents

étale morphism (submersion, immersion)

generally in differential cohesion

• reduction modality$\dashv$ infinitesimal shape modality

• formally étale (formally smooth, formally unramified)

• étale topos

• étale homotopy

• étale cohomology

• étale ∞-groupoid

in topology

• local homeomorphism, étale space

• étale groupoid

in differential geometry

• local diffeomorphism, (submersion, immersion of smooth manifolds)

• étale Lie groupoid

in algebraic geometry

• étale morphism of schemes, formally étale morphism of schemes

• étale site, pro-étale site, étale (∞,1)-site

• Deligne-Mumford stack

• ℓ-adic cohomology