An analogue of Kida's formula for elliptic curves with additive
reduction
An analogue of Kida's formula for elliptic curves with additive
reduction
We study the Iwasawa theory of $p$-primary Selmer groups of elliptic curves $E$ over a number field $K$. Assume that $E$ has additive reduction at the primes of $K$ above $p$. In this context, we prove that the Iwasawa invariants satisfy an analogue of the Riemann--Hurwitz formula. This generalizes a …