jgarnek/de_rham_cyclic
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

X ---> X/C cases

Browse Source
This commit is contained in:
jgarnek 2024-12-18 12:54:34 +01:00
parent a1a831d315
commit d29a4adb22
1 changed files with 10 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

11
article_de_rham_cyclic.tex
View File

@ -924,7 +924,7 @@ Indeed, ????. The ramification points of $\pi : X \to X/G$ are as follows:
\item[] (their stabilizers are subgroups $C_1 = C$, $\ldots$, $C_p$ \item[] (their stabilizers are subgroups $C_1 = C$, $\ldots$, $C_p$
conjugated to $C$), conjugated to $C$),
\item point $P_{\infty}$ above $Q_{\infty}$ (its stabilizer is $G$), \item a point $P_{\infty}$ above $Q_{\infty}$ (its stabilizer is $G$),
\item points $P_i^{(1)}, \ldots, P_i^{(p \cdot (p-1))}$ above $Q_i$ for $i = 1, \ldots, N$ \item points $P_i^{(1)}, \ldots, P_i^{(p \cdot (p-1))}$ above $Q_i$ for $i = 1, \ldots, N$
\item[] (their stabilizers equal $C'$). \item[] (their stabilizers equal $C'$).
@ -933,6 +933,15 @@ Indeed, ????. The ramification points of $\pi : X \to X/G$ are as follows:
The same points are in the ramification locus of the morphism $X \to X/C$ with the following The same points are in the ramification locus of the morphism $X \to X/C$ with the following
ramification groups: ramification groups:
% %
\[
C_{P_i^{(j)}} =
\begin{cases*}
C, & \textrm{ if } (i, j) = \\
C', &
\end{cases*}
\]
\begin{align*} \begin{align*}
C_{P_0^{(1)}} &= C\\ C_{P_0^{(1)}} &= C\\
C_{P_0^{(i)}} &= C' \qquad \textrm{ for } i > 1,\\ C_{P_0^{(i)}} &= C' \qquad \textrm{ for } i > 1,\\