Errata and Addenda for Algebraic Geometry II
Here we post a list of errata and addenda. The name tags refer to the people who found the mistake. We are very grateful to all of them. Further remarks and hints - trivial or not - are very welcome.
You can submit errata through the web site (or just send us an email).
Explanation: Major error Minor error Typo/Trivial Remark Unclassified
21 errata listed.
| Page | Description | Submitted by | |
|---|---|---|---|
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p. 7,
¶
Line 2
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Insert `homomorphism' after `$R$-algebra'. | U. Görtz | |
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p. 7,
¶
After Equation (17.1.9)
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In the text, it says "Then $\Omega_{R/A}^1$ is the kernel of the $R$-algebra...", but it should be $\Omega_{A/R}^1$ instead. | Cynthia | |
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p. 23,
¶
Line 4, line 23
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Add periods at the end of sentences. | Erik Nikolov | |
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p. 30,
¶
Exercise 17.9
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The curve should be defined by the homogeneous equation $Y^2Z-X^3-aXZ^2-bZ^3$. The definition of $\omega$ should read $\omega = d(x)/y$ where $x = \frac XZ, y=\frac YZ\in K(E)$. | U. Görtz | |
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p. 35,
¶
Proposition 18.11
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In general, no such global lift $b$ exists. Consider e.g. the case where $f$ is formally smooth but not formally étale: For two distinct global lifts $b_{1}$ and $b_{2}$ of $a_{0}$ take the open cover $U_{1} = U_{2} = T$. Instead, the conclusion that is actually proved (and used in the sequel) is that under the given assumptions there exists a lift $b\colon T\to X$ (i.e., $b$ makes the diagram (18.0.1) commutative). As explained in the preceding discussion, this means that one can change each $b_i$ by a derivation in $\mathscr G(U_i)$ (with notation as in Lemma 18.9) to obtain a family $b_i'$ of lifts $U_i\to X$ that can be glued. |
M. Herbers, J. K. Hessel | |
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p. 50,
¶
Prop. 18.55
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The statement of the proposition is correct, but the proof is incomplete. In fact, the proof of (i) $\Rightarrow$ (ii) only explains the conclusion for $I$ and $B$ as in the definition of a smooth morphism (cf. the beginning of Section (18.10)). To prove the statement in general, one should use that the morphism ${\rm Spec}(A)\to {\rm Spec}(R)$, being smooth at $\mathfrak p$, is formally smooth in a neighborhood of $\mathfrak p$ (Theorem 18.56). Then one can invoke Proposition 18.20. |
U. Görtz | |
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p. 66,
¶
Exercise 18.24
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Replace `Björn Poonen' by `Bjorn Poonen'. | U. Görtz | |
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p. 68,
¶
line 7
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B.58 in " a regular sequence (Definition B.58)" should be B.60, and the reference should be made clickable. | Jinyi Xu | |
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p. 68,
¶
line 4
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B.61 in "By Krull’s principal ideal theorem (Corollary B.61)" should B.64 and the reference should be made clickable. | Jinyi Xu | |
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p. 85,
¶
Line 14
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Replace 'local intersection ring' by 'complete intersection ring'. | U. Görtz | |
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p. 196,
¶
Line 13
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Replace ${\rm Hom}$ by $\mathscr Hom$. | U. Görtz | |
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p. 242,
¶
Theorem 22.22
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In (3) it must say the $R$-submodule instead of $A$-submodule. | T. Wedhorn | |
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p. 278,
¶
Just before proof of Corollary 22.92
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Replace the fact that being “affine” is a stable under fpqc-descent by the fact that being “affine” is a property stable under fpqc-descent | Matthieu Romagny | |
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p. 307,
¶
Line -3 (statement of Cor. 23.18)
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Replace "finite generated" by "finitely generated". | Matthieu Romagny | |
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p. 476,
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Line 5
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Insert `morphism' after `separated' and delete the comma. | U. Görtz | |
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p. 493,
¶
Line -3
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Replace `($S_2$)-module' by `($S_2$)'. | U. Görtz | |
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p. 505,
¶
Line 9
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Replace `12.3 3' by `12.3 (3)'. | U. Görtz | |
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p. 505,
¶
Line 4 of proof of Thm. 25.151
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Replace `Theorem 25.141' by `Corollary 25.141'. | U. Görtz | |
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p. 596,
¶
Line 17
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Replace `Theorem 25.32' by `Section (25.32)'. | U. Görtz | |
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p. 747,
¶
Line 14, 15
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Replace $u$ by $f$ and $\bar{u}$ by $\bar{f}$. | F. Leptien | |
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p. 786,
¶
Line 3
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"to to" should be replaced by "to". | Torsten Wedhorn |