Suppose that $q$ is a rational prime, and $K$ is a $p$-extension over $\Bbb{Q}$ where $p$ is prime, then $q$ ramifies in $K$ if and only if $q$ is $p$ or $q$ is congruent to $1 \mod p$. I don't know why this is true, can someone convince me of this?
ramification in $p$-extensions
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algebraic-number-theory