### 111.5.11 Theorem on formal functions and Grothendieck's Existence Theorem

These papers give generalizations of the theorem on formal functions [III.4.1.5, EGA] (sometimes referred to Grothendieck's Fundamental Theorem for proper morphisms) and Grothendieck's Existence Theorem [III.5.1.4, EGA].

• Knutson: Algebraic spaces [Chapter V, Kn]

Generalizes these theorems to algebraic spaces.
• Abramovich-Vistoli: Compactifying the space of stable maps [A.1.1, abramovich-vistoli]

Generalizes these theorems to tame Deligne-Mumford stacks
• Olsson and Starr: Quot functors for Deligne-Mumford stacks

Generalizes these theorems to separated Deligne-Mumford stacks.
• Olsson: On proper coverings of Artin stacks

Provides a generalization to proper Artin stacks.
• Conrad: Formal GAGA on Artin stacks

Provides a generalization to proper Artin stacks and proves a formal GAGA theorem.
• Olsson: Sheaves on Artin stacks

Provides another proof for the generalization to proper Artin stacks.

There are also:

• 4 comment(s) on Section 111.5: Papers in the literature

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