### 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*[olsson-starr]Generalizes these theorems to separated Deligne-Mumford stacks.

Olsson:

*On proper coverings of Artin stacks*[olsson_proper]Provides a generalization to proper Artin stacks.

Conrad:

*Formal GAGA on Artin stacks*[conrad_gaga]Provides a generalization to proper Artin stacks and proves a formal GAGA theorem.

Olsson:

*Sheaves on Artin stacks*[olsson_sheaves]Provides another proof for the generalization to proper Artin stacks.

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