Geodesic
An analog of the Riemann--Hurwitz formula for one type of $l$-extensions of algebraic number fields
Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 325-347

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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. 
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     author = {L. V. Kuz'min},
     title = {An analog of the {Riemann--Hurwitz} formula for one type of $l$-extensions of algebraic number fields},
     journal = {Izvestiya. Mathematics },
     pages = {325--347},
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     volume = {36},
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     year = {1991},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a5/}
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L. V. Kuz'min. An analog of the Riemann--Hurwitz formula for one type of $l$-extensions of algebraic number fields. Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 325-347. http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a5/