Popescu's theorem

In commutative algebra and algebraic geometry, Popescu's theorem, introduced by Dorin Popescu,[1][2] states:[3] For example, if A is a local G-ring (e.g., a local excellent ring) and B its completion, then the map A → B is regular by definition and the theorem applies.

Another proof of Popescu's theorem was given by Tetsushi Ogoma,[4] while an exposition of the result was provided by Richard Swan.

[5] The usual proof of the Artin approximation theorem relies crucially on Popescu's theorem.

Popescu's result was proved by an alternate method, and somewhat strengthened, by Mark Spivakovsky.

[6][7] This algebraic geometry–related article is a stub.