  We show that Riemann-Hurwitz-style translation formulas obtained by Kuz'min,
Kida, Iwasawa, Wingberg et alii for the lambda invariant attached to certain
Iwasawa moduli in cyclotomic Z{\ell}-extension of number fields are essentially
equivalent. More precisely, we prove that all these formulas,including those
stated in terms of representations, resul tidentically for purely algebraic
reasons from the arithmetic computation of a suitable Herbrand quotient which
it suffices to carry out in the cyclic case of prime degree {\ell}.
