Addenda and Errata (Books)
Last revised February 16, 2009.
Addenda and errata for my books. See elsewhere for an errata for my articles and
1980 Etale Cohomology, Princeton U. Press.
px, yt, zb means page x, line y from top, line z from bottom.
pxiii. The only reason I assumed all the schemes are locally Noetherian was that I
didn’t want to keep saying finite presentation etc. for finite type. I can’t believe it really
matters anywhere. The fibre product schemes on p. 70, line 2, and p80 are not automati-
cally Noetherian. If I remember correctly, Grothendieck’s example of naturally arising non-
noetherian rings is the tensor product of two completions of ring. Products of Henseliza-
tions are probably only about as Noetherian as completions.
p6. Hochster has questioned whether the proof in Raynaud is correct.
p6, 18b. It does not “follow easily”. In fact, passing from the affine result to the global
result is not easy.
p7, 1.12. Cf. Hartshorne, Algebraic Geometry, Ex. 3.7. (Hartshorne’s book appeared
just before I sent the final version of the manuscript to the publisher, in time only for me to
change some of the references in the manuscript.)
p7, 12b. Atiyah-Macdonald [1, 2.19]
p9. Correct statement of 2.5: Let˛ A! B be a flat A-algebra, and consider b 2 B . If
the image of b in B=˛□1.n/ is not a zero-divisor for any maximal ideal n of B , then B=.b/
is a flat A-algebra. This necessitates some changes on p10.
p16. For the proof of Theorem 2.16, see also Mumford [2, p57].
p31. In Exercise 3.27, the Y should be T .
p40. Remark 5.1c should read: ...states that the functor that...
p42. Chinberg criticizes the statement of Abhyankar’s theorem (first paragraph) as
being too global to be true.
p47, 5t. Drop the condition:“closed under fiber products”. It is not actually needed,
and it fails for the small flat site: U; V;W can all be flat over X without U V W being flat
over X (the point is that U ! V need not be flat).
p51, 11b. Should be (I.2.19).
p57. The first line should read