p71. In the proof of Prop. 18.14, I claim that n=m(k^{al}\otimes A) is a maximal ideal; but this is only true if m corresponds to some k-valued point of A, i.e., if A/m=k (Chun Yin, Hui). To fix this, let n be a maximal ideal of (k^{al}\otimes A), and let m be the intersection of n with A. Then the displayed equation is true if the tensor product is taken over A/m; in the next line, k should be replaced with A/m. [In fact, the whole proof should be rewritten and completed.]
From Bhupendra Nath Tiwari (corrections in red).
p.4 Proposition 2.1 ... Proof. Similarly if b^{\prime} is not in c, then there exists an f^{\prime}
such that f = c^{\prime}+ a^{\prime} b^{\prime} with c^{\prime} \in c.
p.9 proposition 3.3 .... M is noetherian if and only both N and M/N are noetherian.
p.22 Proposition 6.3 ... Proof. .... , but the next lemma shows, some is retained.
p.40 Lemma 10.9 ... Proof. ... which one checks sends \delta(a) to the endomorphism x ...
p.42. Zariski Lemma. ... When k is infinite, this obvious, because the polynomials ...
p.43 Corollary 11.6 .... Proof. ... , then f \in (X_1- a_1, ... X – a_n).
p.56 Proposition 14.2 ... Proof. ... The shows that rad(q) is primary, and ...
p.65 Proposition 14.2 ... Proof. .. The Noether normalization (see 5.11) shows that..
p.68 In other words, it is the set of equivalence classes of ... are equivalent if f | U'' = f | U''
p.71 Proposition 18.14 ... Proof. ... If V is smooth, then all the local the local rings of ...