Errata — Tome I

Misprints and errors in the new edition of SGA 3, Tome 1.

13 October 2024.

1. SGA 3, Tome 1

Page numbers refer to the version published in 2011. The new compilation compressed the pages to remove the final (odd-numbered) page of Exposés 3 and 6A, so the pagination of the 2024 version is shifted by $-2$ (resp. $-4$) starting from Exposé 4 (resp. Exposé 6B).

1.1. Exposé I

• p. 18, in the added Proposition 3.1.2, the proof that $O$ is a generator is incorrect. This has been corrected in the 13/10/2024 version.
• p. 29, N.D.E. (40): $\dot{CfV}{I}_B$ should be: Cf. VI_B.

1.2. Exposé II

• p. 82: the 2nd sentence of N.D.E. 71 should appear in N.D.E. 72.

1.3. Exposé IV

• p. 182, proof of Prop. 1.8: in the diagram, on the upper-left arrow, vu should be uv, and likewise in the 1st line below the diagram. This has been corrected in the 13/10/2024 version.

1.4. Exposé VI_A

• p. 302, the proof of Lemma 2.1.3 contained an unwarranted simplification; one must revert to the original proof. This has been corrected in the 13/10/2024 version.
• p. 329, in the proof of Lemma 6.1, the word "à droite" (on the right) is missing after "resp.".

1.5. Exposé VI_B

• p. 359, end of Cor. 4.4. There was a slip in N.D.E. (31): keeping the same notation, one must consider the subgroup $G=\mathrm{Spec}A[X]/(\delta X)$ of the additive group over $S$, which to every $A$-algebra $R$ associates the subgroup of $r\in R$ such that $\delta r=0$. This has been corrected in the 13/10/2024 version.
• p. 374, Th. 6.2.3: in the proof, line 2 of the 3rd paragraph, replace "free module" by "projective module".

1.6. Exposé VII_B

• p. 587, line 6 of 5.0: $\Delta (A)$ should be $\Delta (a)$.