An analog of the Riemann–Hurwitz formula for one type of $l$-extensions of algebraic number fields

For an $l$-extension $K/k$ of an algebraic number field satisfying certain appropriate conditions the author obtains a formula analogous to the Riemann–Hurwitz formula. This formula connects the Iwasawa invariants of the fields $k_\infty$ and $K\cdot k_\infty$, where $k_\infty$ is some $\mathbf Z_l$-extension of the field $k$. It is not assumed that $K$ and $k$ are fields of CM-type.