Bourbaki

Proposition 4

Tag 0E2U, permanent. Cite it as [Bourbaki, Tag 0E2U].

Algebra, chapter X, § 9. Complexes de Koszul

For every complex CC, there are exact sequences .

0⟶A/xA⊗AHp(C)⟶Hp(x,C)⟶Hom⁡A(A/xA,Hp−1(C))⟶0. 0\longrightarrow A/xA\otimes_A H_p(C)\longrightarrow H_p(x,C)\longrightarrow \operatorname{Hom}_A(A/xA,H_{p-1}(C))\longrightarrow 0.

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

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Cites

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