Preface
Page IX, line 7: Should be [GeR2]
Section 1
page 16, line 2 from bottom: should be \sum^t_{i=0}\alpha^{r^{t-i}}_i
page 16, line 2 from bottom: the last sum should be \sum_{i=0}^t \alpha_i
\tau^{i-t}
page 21, line 5: should be $$Df=f^\prime+fD\,,$$
page 29, line 6: ``symmetry'' should be replaced by ``reflexivity''
page 29, line 6: ``reciprocity'' should be replaced by ``symmetry''
Section 4
page 82, line -15: R should be {\cal F}
page 83, line 14 should be: c\psi c^{-1}
page 83, line 20 should read: scheme-theoretic kernel of $P$.
page 98, line 14: should be $[D\colon L]=d^2$
page 110, line 23: should read: $$ s=[L\colon \Bbb F_r(F)]\,.$$
page 126, line 12: should be \sum\limits^n_{i=0}\alpha_i \tau^i
page 127, line 7: should read ``..., we obtain''
Section 5
page 150, line 5 should be: \psi_{T}
page 151, line 14: $\dim E=\rank_{L[\tau]}M(E)=w(E)r(E)$
page 158, line 14 should be: (\theta \tau^0+N_n)
page 158, line 15 should be: (\theta \tau^0+N_n)
page 161, line 6: b_j
page 164, line 15 should read: where $e$ is
page 166, line -2 should be: (b\mapsto m(f(b))))
page 171, line 11: should read: \Hom_{\overline{K}[T,\tau ]_0}
page 173, line 13, both copies of (T+N_n) should be: (\theta +N_n)
page 173, line -7, both copies of (T+N_n) should be: (\theta +N_n)
Section 6
page 179, line 10: should be ``will follow''
page 179, line 16: should be R=\bigoplus\limits^\infty_{d=0} R_d
page 185, line 3: ``section'' should be ``sections''
page 186, line 12, should read: \gamma\in H^0(\overline{X}-P,{\cal F})
page 187, line 14 from bottom: should read ``...one can find an element...''
page 188, line -12 should be: R_d/R_{d-1}
page 189, line 6: should be M=L\{\sigma\}
page 190, line 10 from bottom: should be H^0({\cal F}_{n+1}/{\cal F}_n)
page 192, line 5 should be: M_P
Section 7
page 193, line -13 should be: \psi\colon {\bf A}\to L\{\tau\}
page 199, line 4 should be: arbitrary homogeneous. We set
page 201, line 17 should be: \lambda \psi \lambda^{-1}
page 223, line 2 should be: \prodi_{i\in I,\, \deg i\leq N}
page 226, line 6 should be: dj
Section 8,
page 242, line 16: should be ``order of $M$''
page 248: line 6 should be ``. We''
page 248, line 10 should be: f(s)
page 249, line 2: should be ``Thus our''
page 250, line 15 should be: B_{i_j}
page 252, line -14 should be: \sigma ({\bf V})
page 260, line -5 should be: c(a)a^{(-j-j_0)}
page 262, line 8 should be: \cdots - j^h_\alpha
page 263, line 8: should be f(u)
page 264, line -3 should be: \deg (D)
page 268, line -14 should be: and ${\bf H}^+$.
page 269, line 15: should be ``the problem''
page 271, line 5 should be: 8.2.10
page 271, line 14: should be ``Witt ring of the finite''
page 271, line -4 should be: 7.5.5
page 334, line 15: should be Theorem 3.2
page 339, the fourth paragraph from bottom should be:
``Recall that the value field was defined as a subfield of ${\bf C}_\infty$.
Let ${\bf K}_{\bf V}$ be the smallest extension of $\bf K$ containing
$\{\langle I \rangle\}$ for $I\in \cal I$ (= ${\bf K}\cdot \bf V$ if $
d_\infty=1$).
Let ${\bf K}_{\bf V}(\rho)$ be the smallest extension
of ${\bf K}_{\bf V}$ containing the coefficients of the characteristic
polynomials of the Frobenius elements as discussed before 8.10.2. Thus,
for each $y\in {\Bbb Z}_p$, the function $x\mapsto L(\rho,(x,y))$ is given
by a power series in $x^{-1}$ with coefficients precisely in
${\bf K}_{\bf V}(\rho)$. Note that by construction, as $\rho$ is
of Galois type, the field ${\bf K}_{\bf V}(\rho)$
is an unramified finite extension of ${\bf K}_{\bf V}$. Similarly
we let ${\bf V}(\rho)$ be the smallest extension of ${\bf V}$
containing the above coefficients. Again,
${\bf V}(\rho)$ is a finite constant field extension of $\bf V$.''
page 341, line 11: should be \{\beta_1(y),\dots ,\beta_n(y)\}
page 341, line 12: should be L_n((u^y)^{1/p^t}
Section 9
page 356, line 6: should be $$2T^{36}+T^{28}+2T^{18}+T^2$$
page 364, line 5: should be \pi_1^{\deg D_j}D_j
page 366, line 5: should be ``for all $y...''
page 366, line 15: should be = {_t\xi}_{^{\scriptstyle u}}^{-1}
Section 10
page 398, line 7: should be S_m(e_C(\xi x),1
page 398, line 20: should be \left\{S_m(e_C(\xi b/f),1)\right\}