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Proper Morphisms, Completions, and the Grothendieck Existence Theorem

Context

Higher geometry

Higher algebra

This page collects links related to the article

  • Jacob Lurie,

    Proper Morphisms, Completions, and the Grothendieck Existence Theorem

    (pdf)

on basic properties of E-∞ geometry

Contents

1. Generalities on spectral Deligne-Mumford stacks/algebraic spaces

1.1 Points of spectral Deligne-Mumford stacks

1.2 Étale morphisms

1.3 Localic spectral Deligne-Mumford stacks

1.4 Quasi-compactness of spectral Deligne-Mumford stacks

1.5 Local properties of spectral Deligne-Mumford stacks

2. Noetherian approximation

3. Properness

3.1 Strongly proper morphisms

3.2 The direct image theorem

3.3 Proper linear \infty-categories

3.4 Valuative criteria

4. Completions of modules

5. Completions of spectral Deligne-Mumford stacks

5.1 Formal completions

5.2 Truncations in QCoh(𝒳 K )QCoh(\mathcal{X}_K^{\wedge})

5.3 The Grothendieck existence theorem

5.4 Algebraizability of formal stacks

6. Relationship with formal moduli problems

A. Stone duality

category: reference

Last revised on August 26, 2014 at 08:37:12. See the history of this page for a list of all contributions to it.