Joseph Oesterlé says:

p 69, l 26 S contains all v with |alpha_v|_v < 1 should be S contains all v with |alpha_v|_v ≠ 1

p 69, l 27 \frac{1}{2}C should be \frac{1}{2C}

p 131 corollary 2. "Let L/K be an extension" should be "Let L/K be a Galois extension"

p 133 proof of corollary 1 "Note that a less violent" should be "Note that if L/K is Galois, a less violent"

p 157 first line of section 4.2: One has to suppose L/K abelian.

p 209 l 11 to 19 Only the conclusion at the last line seems to be right...