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\begin{flushright}
  Your Name Here
\end{flushright}


\begin{center}
  \textbf{Math 105}\\ Homework 5
\end{center}

\begin{enumerate}

\item (4-1-x) For each rational prime $p\ge 2$, characterize all quadratic extensions $K$ of $\Q_p$.

\item (4-1-x) Let $K$, $L$ be local fields containing $\Q_p$,
  $\varphi:K \to L$ an algebraic isomorphism with
  $\varphi\big|_{\Q_p} = id$.  Show that $\varphi$ is continuous and open.

\item (4-1-x) Let $E/F$ be an extension of local fields.  Say that
  $\alpha \in E$ is integral over $F$ if it is the root of a monic
  irreducible polynomial in $\O_F[x]$.  Show that $\O_E$ equals the
  set of elements of $E$ integral over $F$.

     
\end{enumerate}

\end{document}


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