Cote n° 144 · pages 21–182 · 19 commutative diagrams · [Suite autour de Teichmüller dont] Teichmülleries, 1981-1982 : notes manuscrites (1981-1983, s.d.), lettres (1981, s.d.).
Inventory dating : 1981-1983
Édition de démonstration

batch 2 · p. 21 — read it beside the facsimile1 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\mathfrak{X}_{g,\nu\,\mathbb{Q}} \arrow[d] & \mathfrak{X}_{g,\nu\,K} \arrow[l] \arrow[d] & \mathfrak{X}_{g,\nu\,\overline{K}} \arrow[l, no head] \arrow[d] & \mathfrak{X}_{g,\nu\,k} \arrow[l, no head] \arrow[d] \\
M_{g,\nu\,\mathbb{Q}} \arrow[d] & M_{g,\nu\,K} \arrow[l] \arrow[d] \arrow[u, dashed, bend right=40] & M_{g,\nu\,\overline{K}} \arrow[l, no head] \arrow[d] & M_{g,\nu\,k} \arrow[l, no head] \arrow[d] \\
\mathbb{Q} \arrow[r, no head] & K \arrow[r, no head] \arrow[u, dashed, bend left=40] & \overline{K} \arrow[r, no head] & k
\end{tikzcd}
batch 2 · p. 22 — read it beside the facsimile2 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
 & 1 \arrow[d] & 1 \arrow[d] & & \\
 & \pi_{X,x} \arrow[r, no head, "="] \arrow[d] & \pi_{X,x} \arrow[d] & & \\
1 \arrow[r] & \mathfrak{G}_{X,x} \arrow[r] \arrow[d] & \mathcal{M}_{X,x,K} \arrow[r] \arrow[d] & \Gamma_{\overline{K}|K} \arrow[r] \arrow[d, no head, "\parallel"] & 1 \\
1 \arrow[r] & \mathcal{T}_{X} \arrow[r] \arrow[d] & \mathcal{N}_{X,x,K} \arrow[r] \arrow[d] & \Gamma_{\overline{K}|K} \arrow[r] & 1 \\
 & 1 & 1 & &
\end{tikzcd}
batch 2 · p. 23 — read it beside the facsimile3 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
1 \arrow[r] & \mathfrak{G}_{X,x} \arrow[r] & \mathcal{M}_{X,x} \arrow[r] & \Gamma_{\widetilde{\mathbb{Q}}/\mathbb{Q}} \arrow[r] & 1 \\
1 \arrow[r] & \mathfrak{G}_{X,x} \arrow[r] \arrow[u, no head, "\parallel"] & \mathcal{M}_{X,x,K} \arrow[r] \arrow[u, "\mathrm{cart}"'] & \Gamma_{\overline{K}/K} \arrow[r] \arrow[u] & 1
\end{tikzcd}
batch 2 · p. 23 — read it beside the facsimile4 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
1 \arrow[r] & \mathcal{T}_{X,x} \arrow[r] & \mathcal{N}_{X,x} \arrow[r] & \Gamma_{\widetilde{\mathbb{Q}}/\mathbb{Q}} \\
1 \arrow[r] & \mathcal{T}_{X,x} \arrow[r] \arrow[u, no head, "\parallel"] & \mathcal{N}_{X,x,K} \arrow[r] \arrow[u, "\mathrm{cart}"'] & \Gamma_{\overline{K}/K} \arrow[u]
\end{tikzcd}
batch 2 · p. 24 — read it beside the facsimile5 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
\mathcal{M}_{X,x} \arrow[r] & \Gamma_{\widetilde{\mathbb{Q}}/\mathbb{Q}} \\
 & \Gamma_{\overline{K}/K} \arrow[u] \arrow[ul, dashed]
\end{tikzcd}
batch 2 · p. 24 — read it beside the facsimile6 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
\mathcal{N}_{X,x} \arrow[r, two heads] & \Gamma_{\overline{\mathbb{Q}}/\mathbb{Q}} \\
 & \Gamma_{\overline{K}/K} \arrow[u] \arrow[ul, dashed]
\end{tikzcd}
batch 2 · p. 26 — read it beside the facsimile7 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\operatorname{Isom}_{*}(\overline{K},\overline{K}') \times \operatorname{Disc}(\overline{K}) \arrow[r] & \operatorname{Disc}(\overline{K}') \\
\operatorname{Isom}_{*}(\overline{K},\overline{K}') \times \operatorname{Hom}(\overline{K},\mathbb{C}) \arrow[r] \arrow[u] & \operatorname{Hom}(\overline{K}',\mathbb{C}) \arrow[u]
\end{tikzcd}
batch 2 · p. 30 — read it beside the facsimile8 / 19
LaTeX source
\begin{tikzcd}
\pi^{\tau}_{0,3} \arrow[r, "\varphi"] \arrow[d] & \mathrm{Gl}(2,\mathbb{Z}) \arrow[d] \\
\pi_{0,3} \arrow[r, "\varphi^{0}"] & \mathrm{Sl}(2,\mathbb{Z})
\end{tikzcd}
batch 2 · p. 38 — read it beside the facsimile9 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=large]
 & \varepsilon_\infty \arrow[dl, no head, "\sigma_1"'] & \\
\varepsilon_0 \arrow[rr, "\sigma_\infty"'] & & \varepsilon_1 \arrow[ul, "\sigma_0"']
\end{tikzcd}
batch 3 · p. 41 — read it beside the facsimile10 / 19
LaTeX source
\begin{tikzcd}[column sep=large]
  PM_{1,1} \arrow[d] & P\mathcal{D} \arrow[l] \arrow[d, "{(z_{1},z_{2}) \mapsto z_{2}/z_{1}}"] \\
  M_{1,1} & \mathcal{D} \arrow[l, "{\text{gal.\ groupe } \mathrm{Sl}(2,\mathbb{Z})}"']
\end{tikzcd}
batch 3 · p. 49 — read it beside the facsimile11 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  gx \arrow[r, "\ell"] & y & \\
  & g'y \arrow[r, "\ell'"] & z
\end{tikzcd}
batch 4 · p. 80 — read it beside the facsimile12 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
 & \Pi \arrow[dl, hook] \arrow[dr, hook] & \\
 \Pi^{\mathbb{D}} \arrow[dr, hook] & & \Pi^{\tau} \arrow[dl, hook] \\
 & \Pi^{\mathbb{D},\tau} &
\end{tikzcd}
batch 7 · p. 125 — read it beside the facsimile13 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
\mathcal{M}^!_0 \arrow[r, no head, "2"] \arrow[d, no head, "4"'] & \underline{\mathcal{M}}^! \arrow[r, no head, "6"] \arrow[d, no head, "4"'] & \mathcal{M} \arrow[d, no head, "4"] \\
\underline{\mathcal{M}}^{!\circ}_0 \arrow[r, no head, "2"] \arrow[d, no head] & \underline{\mathcal{M}}^{!\circ} \arrow[r, no head, "6"] \arrow[d, no head] & \underline{\mathcal{M}}^{\circ} \\
1 \arrow[r, no head, "2"] & \mu &
\end{tikzcd}
batch 7 · p. 129 — read it beside the facsimile14 / 19
LaTeX source
\begin{tikzcd}[column sep=small]
a \arrow[r, "{l''}"] & \gamma''^{-1}(a) \arrow[r, "{\gamma''^{-1}(l')}"] & (\gamma'\gamma'')^{-1}(a) \arrow[d, "{(\gamma'\gamma'')^{-1}(l)}"] \\
 & & (\gamma\gamma'\gamma'')^{-1}(a)
\end{tikzcd}
batch 7 · p. 135 — read it beside the facsimile15 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\mu_\tau \arrow[rr, hook, "2"] \arrow[dd, no head, "2"'] \arrow[dr, hook, "2"] & & D_\tau = \mu_\tau\times\mu \arrow[dr, hook, "2"] \arrow[dd, no head, "2"'] & \\
 & \mathfrak{S}^!_0 = \Pi'_0 \arrow[rr, hook, "2"] \arrow[dd, no head, "2"'] & & \Pi' = \Pi'_0\times\mu = \mathfrak{S}^! \arrow[dd, no head, "2"] \\
\{1\} \arrow[rr, hook, "2"] \arrow[dr, hook, "2"] & & \underline\mu \arrow[dr, hook, "2"] & \\
 & \mathfrak{S}^{+!}_0 = \Pi_0 \arrow[rr, hook, "2"] & & \Pi = \Pi_0\times\mu = \mathfrak{S}^{+!}
\end{tikzcd}
batch 7 · p. 135 — read it beside the facsimile16 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\mathfrak{S}^! \arrow[r, hook, "6"] \arrow[d, hook] & \mathfrak{S} \arrow[d, no head, "2"] \arrow[dr, hook] & \\
\mathcal{M}^! \arrow[rr, hook, "6"] \arrow[d, no head, "\hat{\mathbb{Z}}^*"'] & \mathfrak{S}^+ \arrow[dr, hook] & \mathcal{M} \arrow[d, no head, "\hat{\mathbb{Z}}^*"] \\
\mathcal{M}^{+!} \arrow[rr, hook, "6"] & & \mathcal{M}^+
\end{tikzcd}
batch 7 · p. 135 — read it beside the facsimile17 / 19
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\mathcal{M}(0) \arrow[r, leftrightarrow] \arrow[d, no head] & \mathcal{M}^{\Pi}[0] \arrow[rr, hook] \arrow[d, no head] \arrow[dr, hook, "6"] & & \mathcal{M}^! \arrow[dr, hook] \arrow[d, no head] & \\
\mu_\tau \arrow[r, hook] \arrow[d, no head] & D^{\Pi}_0 \arrow[d, no head] \arrow[dr, hook, "2"] & \mathcal{M}^{\mathfrak{S}}[0] \arrow[d, no head] & \Pi' = \mathfrak{S}^! \arrow[dr, hook] \arrow[d, no head] & \mathcal{M} \arrow[d, no head] \\
\{1\} \arrow[r, hook, "\hat{\mathbb{Z}}"] & L^{\Pi}_0 \arrow[dr, hook, "2"] & D^{\mathfrak{S}}_0 \arrow[d, no head] & \underline\Pi = \mathfrak{S}^{+!} \arrow[dr, hook, "6"] & \mathfrak{S} \arrow[d, no head] \\
 & & L^{\mathfrak{S}}_0 & & \mathfrak{S}^+
\end{tikzcd}
batch 10 · p. 181 — read it beside the facsimile18 / 19
LaTeX source
\begin{tikzcd}
\widetilde{D} \arrow[r, hook] \arrow[dr, "\text{surj}"'] & \widetilde{D} \amalg S \arrow[r, "\text{surj}"] & \pi_0(\widetilde{X}) \arrow[r, "g"] & \mathbb{N} \\
 & D & &
\end{tikzcd}
batch 10 · p. 182 — read it beside the facsimile19 / 19
LaTeX source
\begin{tikzcd}
\widetilde{D} \arrow[r, hook, "\text{can}"] \arrow[dr, "q\ (\text{surj})"'] & \widetilde{D} \amalg \widetilde{S} \arrow[r, "p\ (\text{surj})"] & \Delta \arrow[r, "g"] & \mathbb{N} \\
 & D & &
\end{tikzcd}