Processing math: 15%

p 177: "For any absolute value" probably vMk, where k is the splitting field of Q(x), since one applies it to all xi simultaneously.

p 180: Remark B.2.7 has parts (i), (ii), (2).

p 181: vMkεv(r)nv=vMkrnv=r[k:Q] should be vMkεv(r)nv=vMkrnv=r[k:Q]

p 184: In Theorem B.3.2(b) need to assume ϕ(V).

p 190: Top display should read h_{V,D} = h_{V,\phi^*H} = h_{{\mathbb P}^n,H}\circ\phi+O(1) = h\circ\phi+O(1).

p 195: In Theorem B.4.1, V should probably be projective.

p 198: The proof of B.4.2(b) is missing. (By (a) the preperiodic points satisfy \hat h_{V,\phi,D}(P) = 0 hence h_{V,D}(P)=O(1). By the finiteness property the set of rational preperiodic points is finite.)

p 200: Statement (b) follows from (d), so it is natural to prove in the order (a),(c),(d),(b),(e).

p 321: the last two displays should be \partial_{i_1,\ldots,i_m} P.

p 328 bottom inequality is reversed

p 329: The first equation in D.6 in display mode should say: for all i/r < I

p 330: The first equation in display mode should say: for all i/r < I
In the sentence starting: "On the other hand, we know from above …" it should say i < r I and j+1 < r I
The displayed equation that comes after the sentence "Eliminating \beta_2 from these …" should say "for all i < r I, j < r I +1".
Right after that, it should say "it follows that \partial_k W(\beta_1) =0 for all k < r I - 1".

p 331: It says "Now let \phi_1, \phi_2, …, \phi_k\in K(X) be rational functions...", but it should say "Now let \phi_1, \phi_2, …, \phi_k \in K(X_1, X_2, …, X_m) be rational functions…".

p 336: definition of W, second line the sum term of \phi_r - the parentheses are not balanced.

P 376 line 1 and page 378 line 2 from bottom the constant s should be M

P 377 first display second line should have \delta_2, as in =\delta_1h(\phi_{NA}(z)) + \delta_2h(\phi_{NA}(w))

P 377 first display second line should have \delta_2, as in =\delta_1h(\phi_{NA}(z)) + \delta_2h(\phi_{NA}(w))

P 394 paragraph "The fact that": the property that the coefficient of the monomial x_j^N is nonzero follows from the assumption in E.2.2(i) that C does not meet codimension-2 strata.

P 423 display two lines below (96): =\frac{2|z|^2}{|w|^2} should be an inequality \leq\frac{2|z|^2}{|w|^2}.

P 423 bottom display and P 424 top display and following line: 4N should probably be 12N

p 405, inequalities (43),(45),(46) - it seems the inequality should be still an equality, as it seems that the estimation starts on the next page only.

p 420, Equation (87), the \xi_1 and \xi_2 should probably be in the subscript: \deg_{\xi_1}(Q) \leq Nd_1 etc.

Still p 420, on the next display, the statement in B.7.2 doesn't seem to imply precisely what is asked for.