Corollary 3
Tag 0D5R, permanent. Cite it as [Bourbaki, Tag 0D5R].
Commutative Algebra, chapter X, § 4. Anneaux réguliers
Every finitely generated reflexive module over a regular noetherian local ring of dimension 2 is free.
In fact, a regular noetherian local ring is integrally closed (VIII, § 5, No. 2, cor. 1 of th. 1). Corollary 3 therefore follows from corollary 2 and § 1, No. 10, prop. 16.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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