p.449, line -7  Recall also that $\mu_F$ is a finite cyclic group.
p.450, line +2  We extend the norm multiplicatively to the group of fractional ideals. 
p.453, line +8 ...product on the $F_{\RR}$-module $L\otimes_{\ZZ}\RR$... 
p.454, line -13  Every rank $1$ projective $O_F$-module $L$ is a submodule of a $1$-dimensional     
        $F$-vector space. Therefore we may assume ... etc
p.459, line +18 Put $x=1$ here.
p.460  line +3  log u_{\sigma} rather than log(sigma(u))
p.460, line +7: log u' \equiv log u modulo \Lambda in summation.
p.461, line -3 log u_{\sigma} rather than log(sigma(u))
p.461, line -1  log \sigma(\varepslion)u_{\sigma} in summation.
p.463, line +10: overline{d}(fI^{-1})  rather than d(f)
p.464, line +6  volume of T^0  (rather than Pic^0)
p.468, line +2  strict inequality
p.469, line +7  \sum (deg\sigma)y_{\sigma}  in summation
p.473, line  +3  generated by $a$ and $(-b + sqrt(\Delta))/2$.
p.473, line-13  generated by $a$ and $(-b +sqrt(\Delta_F})/2$
p.473, line -1  last line $D = D' -(f) ...$
p.474  line +1  + sign in formula
p.474, line +3  $||v||_Pic = \sqrt{2} * log ...$    (rather than  = 2^{-3/2})
p.477, line +11  $f>1$ rather than $f>0$
p.477, line -10  $a>\sqrt{\Delta/3}$ rather than $a\ge\sqrt{\Delta/3}$
p.483, line +15 We have $D=(I,N(I)^{-1/n})+(O_F,vN(I)^{1/n})$. We compute
                reduced divisors close to $D=(I,N(I)^{-1/n})$ and to
                $(O_F,vN(I)^{1/n})$.
p.483, line +19 close to $({\goth p},N({\goth p})^{-1/n})$
p.483, line +21 close to $(I,N(I)^{-1/n})$
p.483, line -13 close to the divisor $(O_F, v')$ with $|N(v')|=1$.
p.483, line -11 $w^{2^t}=v'$.