All Questions

Let $\mathbb{Q}_{p}$ be a p-adic field such that $ p \neq 2 $. We knew that for every $ n=2m $ there exists exactly one unramified extension $ K $ of $ \mathbb{Q}_{p} $ of degree $ n $, obtained by ...

Let $p$ be a prime, and let $K/\mathbb{Q}_p$ be a tamely ramified finite extension of degree $n$. Let $q$ be a prime factor of $n$ with $q\neq p$. Must there exist an intermediate extension $L$ (...

Let $F$ be a p-adic field (finite extensions of $\mathbb{Q}_p$ for some prime $p$), and $E/F$ be a quadratic extension. Use $\sigma$ to denote the nontrivial element in the Galois group $Gal(E/F)$. ...

Let F be a totally real number field such that the Leopoldt conjecture holds at a prime number $p$ and $M$ be a quadratic totally real extension of $F$. Is there a bound of the Leopoldt defect of $M$ ...