Example

Tag 0E2S, permanent. Cite it as [Bourbaki, Tag 0E2S].

Algebra, chapter X, § 9. Complexes de Koszul

Take $M = k[T_1, ..., T_n]$ ; the Koszul complex $K (\partial/\partial T, M)$ associated with the sequence of endomorphisms $(\partial/\partial T_1, ..., \partial/\partial T_n)$ is identified with the de Rham complex of $k[x_1, ..., x_n]$ over $k$ (X, p. 44): with $m \in C_{\{1,...,n\}}^p(M)$ , we associate the differential form

\omega(m) = \sum_{\alpha_1 < ... < \alpha_p} m(\alpha_1, ..., \alpha_p)\ dx_{\alpha_1} \wedge ... \wedge dx_{\alpha_p},

cf. formula (12) and Example 1, p. 44.

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

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