Algebraic Number Theory
《Algebraic Number Theory》 · 第 394 页 · Chapter VI，Section 5，Exercise 4 后 Problem
For the $p$-adic unit rank $r_p(E)$, the Leopoldt conjecture states $r_p(E)=r+s-1$, where $r$ and $s$ are the numbers of real and complex places; equivalently, $\operatorname{rank}_{\mathbb Z_p}G(M_p/K)=s+1$.