**p.26.** Proposition 1.65. The proof of (a) is a little confusing: one should choose $U$
before passing to the algebraic closure.

**p.51.** Replace $X$ with $G$ twice in the first paragraph of Section 2g.

**p.80, 3.52.** Two inner forms $(G,f)$ and $(G',f')$ are said to be equivalent if
there exists an isomorphism $\varphi:G\to G'$ such that $f'=\varphi_K\circ f$

*up to an inner automorphism of $G_K$ .*
**p.85.** $G_W$ is the stabilizer of $W$ in $G$ (not $V$).

**p.129.** Conrad has questioned 6.18 and 6.19 (see also Waterhouse 1979, 10.1) in the nonsmooth case (see Conrad's comments below).

**p.136.** In the example 6.48, take $p=2$, otherwise the multiplication doesn't preserve the defining relation. See 25.38 for more general examples.

**p.166, footnote.** It would be better to define the eigenvalues of an endomorphism to be the

*multiset* (rather than family) of roots...

**p.173, 9.25.** $\lambda_X$ should lie in $\text{End}(\omega(X))...$, not $\text{End}(X)...$

**p.223.** Proposition 11.36 should read $\ldots \alpha=\text{Lie}(\varphi)$ not
$\ldots \alpha=\text{Lie}(\varphi)\circ\text{Lie}(\varphi)$.

**p.224.** The Verschiebung morphism. In this section, $G$ is commutative. In definition 11.39 the second arrow
should be reversed.

**p.324.** In the last sentence of first paragraph, replace "diagonalizable" with "trigonalizable".

**p.330.** Near the end of 16.20, the field $k'$ is $k[c^{1/p}]$.

**p.360.** The statement before 17.28 should say that $\text{SL}_2$, not $\text{SL}_3$, has dimension $3$.

**p.389.** In the statement of 18.8, the target of $\alpha$ is $G'$, not $G$. This is correct in the diagram.

**p.399 and p.442.** In definition 19.8 and note 21.57, replace "proper normal" with "smooth connected proper normal".

**p.456 et seq.** I sometimes write "isogeny" when I should write "central isogeny", e.g., in the first
paragraph on p.456. It is the central isogenies that preserve the Dynkin diagram and, in general,
behave as isogenies in characteristic zero. See the discussion pp.493--494. I'll try to track down more examples.

**p.457.** In 21.96, replace $\text{SL}_n$ and $\mathbb{Z}/n\mathbb{Z}$ with $\text{SL}_{n+1}$ and $\mathbb{Z}/(n+1)\mathbb{Z}$.

**p.459.** Set braces are missing in the lines displaying $\Phi$ and $\Delta$ in 21.97, 21.98, 21.99,
and an equality symbol is missing for $\Delta$ in 21.98.

**p.460.** In the Example ($D_n$), $\text{SO}_n$ should be $\text{SO}_{2n}$ and,
two lines later, $\text{SO}_{2n+1}$ should be $\text{SO}_{2n}$.

**p.461.** Exercise 21-2 needs an additional hypothesis to exclude the examples in 18.5.

**p.480.** Just after Remark 23.49, replace 18.23 with 18.24.

**p.499.** In 23.50, $\underline{\text{Hom}}(G,H)$ will not be affine when $\underline{\text{Out}}(G)$ is not finite (because
$(\mathbb{Z})_k$ is not affine).

**p.506.** In the condition (c), replace $\beta_R$ with $\beta$. In the next line, replace $\mathfrak{g}_R$ with $\mathfrak{g}_\mathcal{R}$.

**p.518.** In Section 24d, the algebras $A$ over $k$ are required to be nonzero.

**p.518.** "... which are proved in Jacobson 1989", or maybe not --- see Conrad's comments (the statements are true!).

**p.531.** In 24.58 and 24.59, assume $(V,q)$ is regular; in 24.58(b), exclude the case $n=1,\,q=0$.

**p.531.** At the end of the first paragraph of Section 24i, replace $C(V,q)$ with $C_0(V,q)$.

**p.545 et seq.** In 25.6(b), in the final sentence of 25.24, and in 25.27, the
parabolic subgroup ($P$ or $Q$) should be minimal, and in 25.27, $S$ should be maximal split in $P$.

**p.546.** The proofs of 25.7 and 25.10 are incomplete. Also, "nontrivial" on the first line of the proof of 25.10 should be "noncentral".

**p.549.** The assertion 25.16(a), that the relative root system really is a root system, is true, but the standard proofs of this
in the old literature are either false or incomprehensible (see Conrad's comments).

**p.549.** In line 1 of 25.19, add "torus" to "maximal split".

Seven pages of comments and corrections from Brian Conrad can be found here.

**21.01.18.** I removed these because they contain errors. In particular, the statements 1.65, 1.70, 1.71, 7.4, 7.5, 7.6, 7.12, and 17.64 in my book,
their proofs, and their consequences, are correct. Other corrections from Conrad's notes have been listed above.