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I am learning LaTeX. How can I typeset this correspondence?

enter image description here

5

More or less:

\documentclass{article}
\usepackage{mathtools,mathabx}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}

\begin{document}
\[\begin{split}
\left[\parbox{4cm}{\raggedright \emph{Objects:} smooth curves defined over $K$\\ \emph{Maps:} nonconstant \dots}\right]
& \rightsquigarrow 
\left[\parbox{4cm}{\raggedright \emph{Objects:} smooth curves defined over $K$\\ \emph{Maps:} nonconstant \dots}\right]\\
C/K & \rightsquigarrow K(C)\\
\phi: C_1\rightarrow C_2 & \rightsquigarrow \phi^\star: K(C_2)\rightarrow K(C_1)
\end{split}\]
\end{document}

enter image description here

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