Cote n° 143 · pages 1–32
· 11 diagrammes commutatifs · Paradigmes des courbes algébriques (version provisoire) : notes manuscrites (s.d.).
Datation de l’inventaire : [vers 1980-1981]
Édition de démonstration
LaTeX source
\begin{tikzcd}[column sep=large]
(4)\quad \mathcal{G}_{\overline{X}} \arrow[r] & \Gamma \\
& \Gamma_K \arrow[ul] \arrow[u, hook]
\end{tikzcd}LaTeX source
\begin{tikzcd}
(8)\quad \Sigma_{\mathfrak{X}} \arrow[r] & \mathcal{G}_{\mathfrak{X}} \arrow[r] & 1 \\
& \mathcal{G}_{\mathfrak{X}}(\xi) \arrow[ul] \arrow[u, hook]
\end{tikzcd}LaTeX source
\begin{tikzcd}
(9)\quad \mathcal{G}_{\overline{X}} \arrow[r] & \Gamma \\
& \Gamma' \arrow[ul] \arrow[u, hook]
\end{tikzcd}LaTeX source
\begin{tikzcd}
(10)\quad \Sigma_{\mathfrak{X}} \arrow[r] & \mathcal{G}_{\mathfrak{X}} \arrow[r] & \Gamma \\
& & \Gamma' \arrow[ull, "\varphi_{\xi}"] \arrow[u, hook]
\end{tikzcd}LaTeX source
\begin{tikzcd}
(15)\quad \Sigma_{\mathfrak{X}'} \arrow[r] & \mathcal{G}_{\mathfrak{X}'} \arrow[r] & \Gamma \\
& & \Gamma' \arrow[ull, "\varphi_{\xi}"] \arrow[u, hook]
\end{tikzcd}LaTeX source
\begin{tikzcd}
(2)\quad \mathcal{G}' \arrow[r] & \Gamma \\
& \Gamma' \arrow[ul] \arrow[u, hook]
\end{tikzcd}LaTeX source
\begin{tikzcd}
\Sigma' \arrow[r] & \mathcal{G}' \arrow[r] & \Gamma \\
& & \Gamma' \arrow[ull] \arrow[u, hook]
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=large]
\mathrm{Rev}(\Pi) \arrow[r, "F"] & (\mathrm{Ens}) \\
(\pi\text{-}\mathrm{Ens}) \arrow[u, "\simeq"] \arrow[ur, bend right=20] &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=normal, nodes={font=\scriptsize}]
1 \arrow[r] & \pi_1(\overline{M}_{g,\nu;\xi}) \arrow[r] \arrow[d, "\wr"'] &
\pi_1(M_{g,\nu;\xi}) \arrow[r] \arrow[d] & \Gamma \arrow[r] \arrow[drr] & 1 & \\
1 \arrow[r] & \widehat{\mathcal{T}}_{g,\nu} \arrow[r] &
\mathrm{Autext}_{\mathrm{lac}}^{\circ}\bigl(\pi_1(X \smallsetminus \{x_1, \ldots, x_\nu\})\bigr)
\arrow[rrr] & & & \mathrm{Out}\ldots \arrow[d] \\
& & & & & 1
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=tiny, row sep=small, nodes={font=\scriptsize}]
1 \arrow[dr] & & 1 \arrow[dr] & & & & & & \\
1 \arrow[r] & \pi_1(\overline{X}_\xi \smallsetminus S_\nu) \arrow[rr] \arrow[dr] & &
\pi_1(\overline{X}_\xi \smallsetminus S_\nu) \arrow[rr] \arrow[dr] & & 1 \arrow[dr] & & & \\
& 1 \arrow[r] & \pi_1(\overline{M}_{g,\nu+1}) \arrow[rr] \arrow[dr] & &
\pi_1(M_{g,\nu+1}) \arrow[rr] \arrow[dr] & & \Gamma \arrow[r] \arrow[dr] & 1 & \\
& & 1 \arrow[r] & \pi_1(\overline{M}_{g,\nu}) \arrow[rr] \arrow[dr] & &
\pi_1(M_{g,\nu}) \arrow[rr] \arrow[dr] & & \Gamma \arrow[r] \arrow[dr] & 1 \\
& & & & 1 & & 1 & & 1
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=tiny, row sep=small, nodes={font=\scriptsize}]
1 \arrow[dr] & & 1 \arrow[dr] & & & & & & \\
1 \arrow[r] & \widehat{\pi}_{g,\nu} \arrow[rr, "\sim"] \arrow[dr] & &
\widehat{\pi}_{g,\nu} \arrow[rr] \arrow[dr] & & 1 \arrow[dr] & & & \\
& 1 \arrow[r] & \widehat{\mathcal{T}}_{g,\nu+1} \arrow[rr] \arrow[dr] & &
\mathrm{Aut}_{\mathrm{lac}}^{\circ}(\widehat{\pi}_{g,\nu})^{!} \arrow[rr] \arrow[dr] & &
\Gamma \arrow[r] \arrow[dr, no head, "=" description] & 1 & \Sigma_{\nu+1} \\
& & 1 \arrow[r] & \widehat{\mathcal{T}}_{g,\nu} \arrow[rr] \arrow[dr] & &
\mathrm{Autext}_{\mathrm{lac}}^{\circ}(\widehat{\pi}_{g,\nu})^{!} \arrow[rr] \arrow[dr] & &
\Gamma \arrow[r] & 1 \quad \Sigma_\nu \\
& & & & 1 & & 1 & &
\end{tikzcd}