Corollary 1

Tag 0CXP, permanent. Cite it as [Bourbaki, Tag 0CXP].

Commutative Algebra, chapter IX, § 3. Corps de représentants

Let $A$ be a separated and complete local ring, whose residue field is an algebraic extension of $\mathbf{Q}$ . Then there exists a unique field of representatives of $A$ . In fact the ring $A$ is of characteristic 0 (no. 1).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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