Indentation problem inside the description environment

Question

I have the following simple code

\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amsfonts,amssymb,amsthm}
\usepackage{enumitem}
\begin{document}

\begin{description}[leftmargin=0.5cm,font=\normalfont\it\bfseries\underline]
\item[Case $1$.] 
\item[Case $2$.] 
\vskip 10pt
\item[]  According to Case $1$ and Case $2$, we must have $\pi_\mathbb{Q}(K)\neq 0$ 
 and $\pi_{\mathbb{Z}_p}(K) \neq 0$ which we consider in the following case.

\vskip 10pt
\item[Case $3$.] 
\end{description}
\end{document}

I need the following behaviour: I need the letter A of 'According' to be aligned with the letter C of 'Case'. When you run this code it seems that the paragraph is shifted a little bit to the right and that the second line of the paragraph is itself shifted to the right. How can I change this?

Another question: As a sort of abbreviation, is it possible to define the item as an option to be 'Case #N' where $N$ counts on positive integers?

Answer 1

You want to define your own environment for this job.

\documentclass[12pt,a4paper]{article}
%\usepackage[utf8]{inputenc}% no longer needed
\usepackage{amsmath,amsfonts,amssymb,amsthm}
\usepackage{enumitem}

\usepackage{showframe}

\newcounter{casedesc}
\newenvironment{casedesc}{%
  \setcounter{casedesc}{0}%
  \begin{description}[style=nextline,leftmargin=0pt,labelsep=0pt]
}{\end{description}}
\newcommand{\case}{%
  \stepcounter{casedesc}%
  \item[\normalfont\itshape\bfseries\underline{Case \textup{\thecasedesc}}]
}

\begin{document}

\begin{casedesc}
\case Some text for this case
\case Some text for this case

According to Case~1 and Case~2, we must have $\pi_\mathbb{Q}(K)\neq 0$ 
and $\pi_{\mathbb{Z}_p}(K) \neq 0$ which we consider in the following case.

\case Some text for this case
\end{casedesc}

\end{document}

I used showframe to see precisely what happens with the margins, remove it for your production version.

For variable representation of the case numbers, you can modify like below.

\documentclass[12pt,a4paper]{article}
%\usepackage[utf8]{inputenc}% no longer needed
\usepackage{amsmath,amsfonts,amssymb,amsthm}
\usepackage{enumitem}

\usepackage{showframe}

\newcounter{casedesc}
\newenvironment{casedesc}[1][\arabic]{%
  \setcounter{casedesc}{0}%
  \let\casenumbering#1\relax
  \begin{description}[style=nextline,leftmargin=0pt,labelsep=0pt]
}{\end{description}}
\newcommand{\case}{%
  \stepcounter{casedesc}%
  \item[\normalfont\itshape\bfseries\underline{Case \textup{\casenumbering{casedesc}}}]
}

\begin{document}

\begin{casedesc}
\case Some text for this case
\case Some text for this case

According to Case~1 and Case~2, we must have $\pi_\mathbb{Q}(K)\neq 0$ 
and $\pi_{\mathbb{Z}_p}(K) \neq 0$ which we consider in the following case.

\case Some text for this case
\end{casedesc}

\begin{casedesc}[\Alph]
\case Some text for this case
\case Some text for this case

According to Case~1 and Case~2, we must have $\pi_\mathbb{Q}(K)\neq 0$ 
and $\pi_{\mathbb{Z}_p}(K) \neq 0$ which we consider in the following case.

\case Some text for this case
\end{casedesc}

\end{document}

After seeing the result, you'll hopefully realize that boldface plus italics plus underlining plus newline is quadruple emphasis.

Here's a version I'd prefer. I also add cleveref to see that you can refer to cases in a simpler way. Apart from \cref and the \label commands, the code hasn't changed.

\documentclass[12pt,a4paper]{article}
%\usepackage[utf8]{inputenc}% no longer needed
\usepackage{amsmath,amsfonts,amssymb,amsthm}
\usepackage{enumitem}

\usepackage{showframe}

\usepackage{hyperref,cleveref}

\newlist{casedesc}{enumerate}{1}
\setlist[casedesc]{
  wide=0pt,
  label=\textbf{\textit{Case} \arabic*.},
  ref=\arabic*,
}
\crefname{casedesci}{Case}{Cases}
\newcommand{\case}{\item}

\begin{document}

\begin{casedesc}
\case\label{cone} Some text for this case
\case\label{ctwo} Some text for this case

According to \cref{cone,ctwo}, we must have $\pi_\mathbb{Q}(K)\neq 0$ 
and $\pi_{\mathbb{Z}_p}(K) \neq 0$ which we consider in the following case.

\case Some text for this case
\end{casedesc}

\end{document}

For variable representation:

\documentclass[12pt,a4paper]{article}
%\usepackage[utf8]{inputenc}% no longer needed
\usepackage{amsmath,amsfonts,amssymb,amsthm}
\usepackage{enumitem}
\usepackage{microtype}

\usepackage{showframe}

\usepackage{hyperref,cleveref}

\newlist{casedesclist}{enumerate}{1}
\setlist[casedesclist]{
  wide=0pt,
}
\newenvironment{casedesc}[1][\arabic]{%
  \casedesclist[label=\textbf{\textit{Case} #1*.},ref=#1*,]%
}{\endcasedesclist}
\crefname{casedesclisti}{Case}{Cases}
\newcommand{\case}{\item}

\begin{document}

\begin{casedesc}
\case\label{cone} Some text for this case
\case\label{ctwo} Some text for this case

According to \cref{cone,ctwo}, we must have $\pi_\mathbb{Q}(K)\neq 0$ 
and $\pi_{\mathbb{Z}_p}(K) \neq 0$ which we consider in the following case.

\case Some text for this case
\end{casedesc}

\begin{casedesc}[\Alph]
\case\label{cthree} Some text for this case
\case\label{cfour} Some text for this case

According to \cref{cthree,cfour}, we must have $\pi_\mathbb{Q}(K)\neq 0$ 
and $\pi_{\mathbb{Z}_p}(K) \neq 0$ which we consider in the following case.

\case Some text for this case
\end{casedesc}

\end{document}

Answer 2

I need the letter A of 'According' to be aligned with the letter C of 'Case'.

Since you employ the enumitem package, I suggest you start the description environment with the options style=nextline and leftmargin=0cm.

\documentclass[12pt,a4paper]{article}
\usepackage{amssymb}
\usepackage{enumitem}
\usepackage[normalem]{ulem} % for '\uline' macro

\begin{document}

\begin{description}[style=nextline,
                    leftmargin=0cm,
                    font=\itshape\uline]
\item[Case \upshape 1.]  
bla bla

\item[Case \upshape 2.] 
According to Case $1$ and Case $2$, we must have 
$\pi_\mathbb{Q}(K)\neq 0$ and $\pi_{\mathbb{Z}_p}(K) 
\neq 0$, which we consider in the following case.

\item[Case \upshape 3.] 
blu blu

\end{description}

\end{document}