The Stacks project

112.5.11 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.