Arithmetic geometry (Storrs, Conn., 1984), 103--150, Springer, New York, 1986.
See xnotes for a corrected version of the article.

Erratum

Some of these may have been corrected in later printings. All have been corrected in the version at www.jmilne.org/math/xnotes/ px, yt, zb means page x, line y from top, line z from bottom.

p104, 2b. Last $w$ in the displayed equation should be $W$.

p119, 9t. Replace \[ \text{dual of }A \] with \[ \text{dual of }B \]

p122, Proposition 12.1. The proof is incomplete if $k$ is not perfect, because then it is not obvious that $B^{\prime}$ is geometrically reduced. (Fixed in xnotes version.)

p124, proof of 12.5. This has been fixed in the xnotes version.

p126, 9t. In the displayed equation $[D:K]$ should be replaced twice with $[D:K]^{\frac{1}{2}}$.

p126, 11t. Should read: nonisomorphic simple representations (insert simple).

p126, 13t. Delete: is defined over $\mathbb{Q}$.

p127, 11t. Replace G with $G$.

p136, 5b. Replace $A$ with $A^{4}$, so that it reads: \[ \ldots\in M_{4}(\mathbb{Z})\subset\mathrm{End}(A^{4}). \]

p137, 6b. Replace subalgebra with subset.

p143, 2b. The line should read: \[ \text{In particular, } |N_{m}-q^{mg}|\leq2gq^{m(g-\frac{1}{2})}+(2^{2g}-2g-1)q^{m(g-1)}. \]

p145, 9t. Remove brackets from the denominator.

p145, 11t. $-\log(1-t)=t+t^{2}+\cdots$