cleveref fails for theorem environments sharing the same counter

I want to number all theorems and corollaries on the same (section) counter. But when I do this, cleveref names them both 'theorem'. Here is a minimal example:

\documentclass{amsart}

\usepackage{amsthm, cleveref}
%\crefname{theorem}{theorem}{theorems}
%\crefname{corollary}{corollary}{corollaries}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}

\begin{document}
\section{Section title}

\begin{theorem}\label{thm:test}
Here is the theorem.
\end{theorem}

\begin{corollary}\label{cor:test}
Here is the corollary.
\end{corollary}

The theorem reference is given by \cref{thm:test} and the corollary reference is given by \cref{cor:test}.

\end{document}

Here, the corollary reference is 'theorem 1.2'. This problem persists even when explicitly stating the crefname.

Any suggestions?