8

I want to design an equation which includes a long down arrow and long up arrow. I'm having just down arrow which is short. I need some help.

enter image description here

7

Just to practice with tikz-cd; the first diagram is in two versions, one with long arrows also in the first half, the second one with shorter arrows where long ones are not needed (just pass over an empty column for lengthening the arrows in the right half).

A similar trick could be used for the second diagram.

\documentclass{article}

\usepackage{amsmath}
\usepackage{tikz-cd}

\DeclareMathOperator{\Frob}{Frob}

\begin{document}

\begin{equation*}
\begin{tikzcd}[column sep=6pc]
C_{(f^{p^n})} \arrow{r} \arrow{d}{(\varphi^n)^*} & 
  k(Z_{f^{(p^n)}}) \arrow{r}{(i_{F^{(p^n)},f^{(p^n)}})^{-1}} \arrow{d}{(\varphi^n)^*} &
  k(X_{F^{(p^n)}}) \arrow{d}{(\varphi^n)^*} \\
C_f \arrow{r} &
  k(Z_f) \arrow{r}{(i_{F,f})^{-1}} &
  k(X_F)
\end{tikzcd}
\end{equation*}
Another diagram
\begin{equation*}
\begin{tikzcd}[column sep=3.5pc]
K \arrow{r}{(\Frob_K)^n} & K^{p^n} \arrow[hookrightarrow]{r} & K \\
k(x) \arrow{r}{(\Frob_{k(x)})^n} \arrow{u} &
k(x)^{p^n} \arrow{u} \arrow[hookrightarrow]{r} & k(x) \arrow{u}
\end{tikzcd}
\end{equation*}

\end{document}

enter image description here

| improve this answer | |
6

There is always an alternative solution!

This example uses amsmath only:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
\begin{array}{ccccc}
C_{(f^{p^n})}& 
\xrightarrow{\phantom{(i_{F^{(p^n)},f^{(p^n)}})^{-1}}}&
k(Z_{f^{(p^n)}})&
\xrightarrow{(i_{F^{(p^n)},f^{(p^n)}})^{-1}}&
k(X_{F^{(p^n)}})\\[0.2cm]
(\varphi^n)^*\left\downarrow\rule{0cm}{1.5cm}\right.\phantom{(\varphi^n)^*}&&
(\varphi^n)^*\Bigg\downarrow\phantom{(\varphi^n)^*}&& 
(\varphi^n)^*\left\downarrow\rule{0cm}{1.2cm}\right.\phantom{(\varphi^n)^*}\\[0.2cm]
C_f&
\xrightarrow{\phantom{texttexttext}}&
k(Z_f)&
\xrightarrow{(i_{F,f})^{-1}}&
k(X_F)
\end{array}
\]

\end{document}

Result:

enter image description here

As you can see, by cleverly using \phantom and \rule, one can get whatever arrow in desired size. However, it usually take too much time to figure out the right size and spacing so it's just not worth it...

| improve this answer | |
6

Using the amscd package the arrows are too short as you see because of the height of the labels on the lower arrows. As standard \smash does not work in this situation, but the mathtools package corrects the definition of \smash. Thus you can code these diagrams as:

Sample output

\documentclass{article}

\usepackage{mathtools,amscd}

\DeclareMathOperator{\Frob}{Frob}

\begin{document}

\begin{equation*}
  \begin{CD}
    C_{(f^{p^n})} @>>> k(Z_{f^{(p^n)}}) @>(i_{F^{(p^n)},f^{(p^n)}})^{-1}>>
    k(X_{F^{(p^n)}}) \\
    @V(\varphi^n)^*VV @V(\varphi^n)^*VV @V(\varphi^n)^*VV \\
    C_f @>>> k(Z_f) @>\smash[t]{(i_{F,f})^{-1}}>> k(X_F)
  \end{CD}
\end{equation*}

\bigskip

\begin{equation*}
  \begin{CD}
    K @>(\Frob_K)^n>> K^{p^n} &\subseteq &K \\
    @AAA @AAA @AAA \\
    k(x) @>\smash[t]{(\Frob_{k(x)})^n}>> k(x)^{p^n}\; &\subseteq &\; k(x).
  \end{CD}
\end{equation*}

\end{document}

Note that I pass the [t] option to \smash killing only the height of the content, not the depth, so that spacing from the horizontal arrow is preserved; alternatively one could write \smash{...}\strut in some situations.

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.