TikZ: node at \item to use in [overlay]

Question

In my beamer presentation I would like to reference an item by pointing an arrow on it's number. However, I don't know how to make \item a TikZ node. Otherwise it works well.

\documentclass{beamer}

\usetheme{Copenhagen}

\usepackage{mathtools}
\usepackage{tikz}
\tikzstyle{every picture}+=[remember picture]

\setbeamertemplate{enumerate items}[square]

\begin{document}

\begin{frame}\frametitle{Title}

\begin{definition}
Let $z\in X^A(\gamma)$.
Then $a_{N-1}\dotsm a_0$ is nice if
\begin{enumerate}
\item $a_{N-1}\neq0$;

\item
\tikz[baseline]\node[anchor=base](t2){};
$z=a_{N-1}\gamma^{N-1}+\dots+a_1\gamma+a_0$;

\item whenever $b_{N-1}\dotsm b_0$ satistfies
\tikz\node[fill=blue,circle](t1){};
, then $b_{N-2}\neq0$.
\end{enumerate}
\end{definition}

\begin{tikzpicture}[overlay]
\path[blue,thick,->] (t1) edge [out=160 , in=340] (t2);
\end{tikzpicture}

\end{frame}

\end{document}

Answer 1

Here is a solution using optional argument of \item:

\item[{\refstepcounter{enumi}%
    \usebeamertemplate{enumerate item}%
    \tikz[baseline]\coordinate(t2);}]%

\documentclass{beamer}

\usetheme{Copenhagen}

\usepackage{mathtools}
\usepackage{tikz}
\tikzstyle{every picture}+=[remember picture]

\setbeamertemplate{enumerate items}[square]

\begin{document}

\begin{frame}\frametitle{Title}

\begin{definition}
Let $z\in X^A(\gamma)$.
Then $a_{N-1}\dotsm a_0$ is nice if
\begin{enumerate}
\item $a_{N-1}\neq0$;

\item[{\refstepcounter{enumi}\usebeamertemplate{enumerate item}\tikz[baseline]\coordinate(t2);}]%
$z=a_{N-1}\gamma^{N-1}+\dots+a_1\gamma+a_0$;

\item whenever $b_{N-1}\dotsm b_0$ satistfies
\tikz\node[fill=blue,circle](t1){};
, then $b_{N-2}\neq0$.
\end{enumerate}
\end{definition}

\begin{tikzpicture}[overlay]
\path[blue,thick,->] (t1) edge [out=160 , in=340] (t2);
\end{tikzpicture}

\end{frame}

\end{document}

Answer 2

Similar to Paul Gaborit's answer by modifying the beamer template for the enumi level. The new template is square tikzmark. Also for testing purposes I've placed the remember picture option manually. And every item can be accessed via the node name

(enummark<item number>)

Here is the code...

\documentclass{beamer}
\usetheme{Copenhagen}
\usepackage{mathtools,lmodern}
\usepackage{tikz}


\defbeamertemplate{enumerate item}{square tikzmark}
{
\usebeamerfont*{item projected}%
\usebeamercolor[bg]{item projected}%
\tikz[remember picture,baseline]{
    \node[fill,
              anchor=base,
                    inner sep=0,
                    text width=2.25ex,
                    text height=1.85ex,
                    text depth=.4ex,
                    align=center]
                    (enummark\insertenumlabel) %Node name
                    {\color{fg}\insertenumlabel}; %Node content
        }
}%
[action]
{\setbeamerfont{item projected}{size=\scriptsize}}

\setbeamertemplate{enumerate items}[square tikzmark]


\begin{document}

\begin{frame}\frametitle{Title}

\begin{definition}
Let $z\in X^A(\gamma)$.
Then $a_{N-1}\dotsm a_0$ is nice if
\begin{enumerate}

\item $a_{N-1}\neq0$;

\item $z=a_{N-1}\gamma^{N-1}+\dots+a_1\gamma+a_0$;

\item whenever $b_{N-1}\dotsm b_0$ satistfies \tikz[remember picture]\node[fill=blue,circle](t1){};, then $b_{N-2}\neq0$.
\end{enumerate}
\end{definition}

\begin{tikzpicture}[overlay,remember picture]
\path[blue,thick,->] (t1) edge [out=160 , in=340] (enummark1);
\path[blue,thick,->] (t1) edge [out=160 , in=340] (enummark2);
\path[blue,thick,->] (t1) edge [out=160 , in=340] (enummark3);
\end{tikzpicture}

\end{frame}

\end{document}