5

For my thesis at university, I'd like to draw a certain diagram, but I am not sure how I should go about it. I have drawn it by hand and it should be displayed down below. I have looked at Tikz/Tikz-cd as well as other questions asked, such as How can I draw commutative diagrams in LaTeX? but mine is a little more sophisticated (as well as the fact it's not a commutative diagram; I couldn't find any other questions that were very similar), and I'm unsure how to draw this diagram due to all the specific details. Could anyone point me in the right direction?

Thank you so much in advance!

This is the diagram I have to draw in LaTeX or Tikz, but I am quite lost.

  • Welcome to TeX.SE. You could use tikz-cd package compatible with your drawing. Your diagram is not sophisticated but it is necessary a long time to realized it. – Sebastiano Apr 10 at 21:11
  • 6
    Hi, welcome. I think tex.stackexchange.com/questions/364415/… has most of the elements needed to make a diagram like that. – Torbjørn T. Apr 10 at 21:11
  • Ah, thanks great, exactly what I was looking for. Thank you so much and have a nice weekend! – Galois Apr 10 at 21:16
12

As pointed out by Torbjørn T. there is no real challenge. At least it is very much simpler to draw such diagrams than to understand Galois theory.

\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}

enter image description here

| improve this answer | |
  • 2
    Flash....but do you have in the your fingers? :-( – Sebastiano Apr 10 at 21:24
  • 4
    @Sebastiano I have claws. And I'd really like to understand Galois theory better. – user194703 Apr 10 at 21:30
  • I'm in love with this figure! Thanks for sharing – user1146332 Apr 10 at 21:48
6

This is a starting point....

\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}

enter image description here

ADDENDUM:

....and here there is my final...destination...

\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}

enter image description here

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