LaTeX/Tikz 中的复杂图表

Question

对于我在大学的论文，我想绘制一个特定的图表，但我不知道该怎么做。我已经手工绘制了它，它应该显示在下面。我查看了 Tikz/Tikz-cd 以及其他问题，例如 如何在 LaTeX 中绘制交换图？ 但我的问题更复杂一些（而且它不是交换图；我找不到其他非常相似的问题），而且由于所有具体细节，我不确定如何绘制此图。有人能给我指出正确的方向吗？

提前谢谢您！

Answer 1

正如 Torbjørn T. 所指出的，这其实并没有什么挑战性。至少绘制这样的图比理解伽罗瓦理论要简单得多。

\documentclass{article}
\usepackage{tikz-cd}
\usepackage{amsmath}
\usepackage{amsfonts}
\DeclareMathOperator{\Frob}{Frob}
\usepackage{dsfont} % I personally like this better than mathbb from AMS
\begin{document}
\begin{tikzcd}[column sep=large]
 T_\ell E(\mathds{F}_p) \arrow[loop below,"\Frob_p"] 
 \arrow[r,"\underset{\sim}{\varphi}"]
 \arrow[r,bend left,"\underset{\sim}{\varphi'}"]
 & (\mathds{Z}_\ell)^2 
 \arrow[loop below,"\psi\circ\Frob_q\circ\psi^{-1}"] 
 \arrow[loop above,"\begin{array}{@{}c@{}}
 \varphi'\circ\Frob_q\circ\varphi^{\prime-1}\\
 \varphi\circ\Frob_q\circ\varphi^{-1}
 \end{array}"] 
 & T_\ell E(\mathds{F}_q) \arrow[loop below,"\Frob_q"] 
 \arrow[l,"\underset{\sim}{\psi}"']
\end{tikzcd}

\bigskip
\begin{tikzcd}[column sep=large]
 T_\ell E(\mathbb{F}_p) \arrow[loop below,"\Frob_p"] 
 \arrow[r,"\underset{\sim}{\varphi}"]
 \arrow[r,bend left,"\underset{\sim}{\varphi'}"]
 & (\mathbb{Z}_\ell)^2 
 \arrow[loop below,"\psi\circ\Frob_q\circ\psi^{-1}"] 
 \arrow[loop above,"\begin{array}{@{}c@{}}
 \varphi'\circ\Frob_q\circ\varphi^{\prime-1}\\
 \varphi\circ\Frob_q\circ\varphi^{-1}
 \end{array}"] 
 & T_\ell E(\mathbb{F}_q) \arrow[loop below,"\Frob_q"] 
 \arrow[l,"\underset{\sim}{\psi}"']
\end{tikzcd}
\end{document}

Answer 2

这是一个起点....

\documentclass[12pt]{article}
\usepackage{mathtools}

\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
A \arrow[r, "\beta"] \arrow["\alpha"', loop, distance=2em, in=305, out=235] \arrow[r, "\gamma", bend left=49] & B \arrow["\delta"', loop, distance=2em, in=305, out=235] \arrow[loop, distance=2em, in=305, out=235] \arrow[loop, distance=2em, in=305, out=235] \arrow[loop, distance=2em, in=305, out=235] \arrow["\overset{p}{q}", loop, distance=2em, in=55, out=125] & G \arrow[l, "\kappa"'] \arrow["u", loop, distance=2em, in=235, out=305]
\end{tikzcd}
\end{document}

附录：

....这就是我的最终...目的地...

\documentclass[12pt]{article}
\usepackage{mathtools}
\usepackage{amssymb}


\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
 T_{l} E(\mathbb{F}_p)  \arrow[r, "\underset{\sim}{\varphi}"] \arrow["\text{Frob}_q"', loop, distance=2em, in=305, out=235] \arrow[r, near start, "\underset{\sim}{\varphi'}", bend left=40] & (\mathbb{Z}_{l})^2  \arrow["\psi\,\circ\,\text{Frob}_q\,\circ\,\psi^{-1}"', loop, distance=2em, in=305, out=235] \arrow["\overset{\scriptstyle \varphi\,\circ\,\text{Frob}_q\,\circ\,\varphi'^{-1}}{\scriptstyle \varphi\,\circ\,\text{Frob}_q\,\circ\,\varphi^{-1}}", loop, distance=2em, in=55, out=125] &  T_{l} E(\mathbb{F}_q) \arrow[l, "\underset{\sim}{\psi'}"'] \arrow["\text{Frob}_q", loop, distance=2em, in=235, out=305]
\end{tikzcd}
\end{document}