Cote n° 147 · pages 5–179 · 49 commutative diagrams · Structure à l'infini des Mg,ν [pages 1 à 90, dont table des matières] : notes manuscrites (s.d.).
Inventory dating : s.d.
Édition de démonstration

batch 1 · p. 5 — read it beside the facsimile1 / 49
LaTeX source
\begin{tikzcd}
Y \setminus I_{k} \arrow[r, "p"] & X \\
\widetilde{A}_{k} \arrow[u, "i"] \arrow[ur, dashed] &
\end{tikzcd}
batch 1 · p. 7 — read it beside the facsimile2 / 49
LaTeX source
\begin{tikzcd}
 & I \arrow[d, "p"] \\
\widetilde{A} \arrow[r, "\sigma"] \arrow[d, "q"'] & S \\
A = \widetilde{A}/\sigma &
\end{tikzcd}
batch 1 · p. 8 — read it beside the facsimile3 / 49
LaTeX source
\begin{tikzcd}
\widetilde{A} \arrow[r, "\sigma"] \arrow[d, "\deg 2"'] & S \\
A &
\end{tikzcd}
batch 2 · p. 30 — read it beside the facsimile4 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
\text{(37)}\quad \hat{M}_{[G]} \arrow[r, hook] \arrow[d, no head, "\wr\ \text{déf}"'] & \hat{M}_{g,\nu} \arrow[d, no head, "\wr"] \\
(\hat{M}_G, \Gamma) & (\hat{M}_{g,I}, \mathfrak{S}_I)
\end{tikzcd}
batch 2 · p. 35 — read it beside the facsimile5 / 49
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\begin{tikzcd}
\text{(43)}\quad \tilde{A}(G') \arrow[r, "\tilde{A}(f)"] \arrow[d, hook] & \tilde{A}(G'') \arrow[d, hook] \\
\mathrm{Fl}(\Pi_1(G')) \arrow[r, "{\mathrm{Fl}(\Pi_1(f))}"] & \mathrm{Fl}(\Pi_1(G''))
\end{tikzcd}
batch 2 · p. 39 — read it beside the facsimile6 / 49
LaTeX source
\begin{tikzcd}
I' \arrow[r, "\sim"] \arrow[d] & I \arrow[d] \\
S' \arrow[r] & S
\end{tikzcd}
batch 3 · p. 42 — read it beside the facsimile7 / 49
LaTeX source
\begin{tikzcd}
\widetilde{B}' \arrow[r, "{\sigma_{G'} | \widetilde{B}'}"] \arrow[d, "\wr"'] & S' = \text{sommets de } G' \arrow[d] \\
\widetilde{A} \arrow[r] & S \simeq \pi_0(G'_{!})
\end{tikzcd}
batch 3 · p. 42 — read it beside the facsimile8 / 49
LaTeX source
\begin{tikzcd}[column sep=large]
G'_{!} \arrow[r, hook, "\text{incl. can}"] \arrow[d, "\text{proj. can}"'] & G' \arrow[d] \\
S = \pi_0(G'_{!}) \arrow[r] & G
\end{tikzcd}
batch 4 · p. 77 — read it beside the facsimile9 / 49
LaTeX source
\begin{tikzcd}
M_{\underline{G}} \arrow[d, hook] \\
\widehat{M}_{\underline{G}} \arrow[r] & \widehat{M}_{\underline{G}'}
\end{tikzcd}
batch 5 · p. 81 — read it beside the facsimile10 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=normal, nodes={font=\scriptsize}]
\Pi M^{*}_{G,G''} \arrow[rr, dashed] \arrow[d, dashed] \arrow[dd, bend right=40, "{\varphi_{G,G''}}"'] \arrow[rrr, bend left=20, "{\gamma_{G,G''}}"] & & \Pi M^{*}_{G',G''} \arrow[r, "{\gamma_{G',G''}}"] \arrow[d] & \Pi M_{G''} \\
\Pi M^{*}_{\underline{G},\underline{G}'} \arrow[rr, "{\gamma_{G,G'}}"] \arrow[d] & & \Pi M_{G'} & \\
\Pi M_{G} & & &
\end{tikzcd}
batch 5 · p. 81 — read it beside the facsimile11 / 49
LaTeX source
\begin{tikzcd}
\Pi M^{*}_{G,G',G''} \arrow[r, "{\gamma_{G,G',G''}}"] \arrow[d, "{\varphi_{G,G''}}"] & \Pi M_{G''} \\
\Pi M_{G} &
\end{tikzcd}
batch 5 · p. 82 — read it beside the facsimile12 / 49
LaTeX source
\begin{tikzcd}
\Pi M^{*}_{G,G''} \arrow[r, "{\gamma_{G'',G}}"] \arrow[d, "{\varphi_{G,G''}}"] & \Pi M_{G''} \\
\Pi M_{G} &
\end{tikzcd}
batch 5 · p. 83 — read it beside the facsimile13 / 49
LaTeX source
\begin{tikzcd}[column sep=small]
\Pi M_{G,G',G''} \arrow[rrr, "{\gamma_{G,G',G''}}"] \arrow[dr] \arrow[dd] & & & \Pi M_{G''} \arrow[dr] & \\
 & \Pi M^{*}_{G,G''} \arrow[rrr, "{\gamma_{G,G''}}"] \arrow[dd] & & & \Pi M_{G''} \\
\Pi M_{G} \arrow[dr, "\mathrm{can}"'] & & & & \\
 & \Pi M_{G,G''} & & &
\end{tikzcd}
batch 5 · p. 85 — read it beside the facsimile14 / 49
LaTeX source
\begin{tikzcd}
S_{A}\Pi M_{G} \arrow[r, "{\tau_{G,G'}}"] \arrow[d] & S_{A'}\Pi M_{G'} \arrow[d] \\
S_{C}\Pi M_{G} \arrow[r] & \Pi M_{G'}
\end{tikzcd}
batch 5 · p. 88 — read it beside the facsimile15 / 49
LaTeX source
\begin{tikzcd}
S\Pi M_{G} \arrow[r, "{S\Pi(f)}"] \arrow[d, "{\varphi_{G}}"'] & S\Pi M_{G'} \arrow[d, "{\varphi_{G'}}"] \\
S_{C}M_{G} \arrow[r, "{\gamma_{f}}"] & \Pi M_{G'}
\end{tikzcd}
batch 5 · p. 94 — read it beside the facsimile16 / 49
LaTeX source
\begin{tikzcd}
I' \arrow[r, hook] \arrow[d] & I \amalg \tilde{A} \arrow[d] \\
S' \arrow[r, hook] & S
\end{tikzcd}
batch 6 · p. 101 — read it beside the facsimile17 / 49
LaTeX source
\begin{tikzcd}
  \widetilde{G}' \arrow[r] \arrow[d] & \widetilde{G} \arrow[d] \\
  G' \arrow[r] & G
\end{tikzcd}
batch 6 · p. 102 — read it beside the facsimile18 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  \Pi_1 M_G \arrow[rr] \arrow[d, "\wr"] & & \Pi_1 M_{G'} \arrow[d, "\wr"] \\
  {\Pi_1 M_{\widetilde{G}} = \prod_{\alpha\in S} M_{g_\alpha, \hat{I}_\alpha}} \arrow[dr] & & {\Pi_1 M_{\widetilde{G}'} = \prod_{\alpha'\in S'} \Pi_1 M_{g'_{\alpha'}, \hat{I}'_{\alpha'}}} \\
  & {\prod_{\alpha'\in S'} M_{g_\alpha, \hat{I}_\alpha}} \arrow[ur, "\Psi"'] &
\end{tikzcd}
batch 6 · p. 104 — read it beside the facsimile19 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  M^{*}_{G, G_{g,I}} \arrow[r, hook] \arrow[dr] & {(M_{G, G_{g,I}}, \Gamma^{!}_{G}) \simeq (M_G, \Gamma^{!}_G)} \\
  & M_{g,I}
\end{tikzcd}
batch 6 · p. 108 — read it beside the facsimile20 / 49
LaTeX source
\begin{tikzcd}[column sep=small]
  d \arrow[r, no head] & d-1 \arrow[r, no head] & 2 \arrow[r, no head] & 1 \arrow[r, no head] & 0
\end{tikzcd}
batch 6 · p. 110 — read it beside the facsimile21 / 49
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\begin{tikzcd}
  d \arrow[r, no head] & \delta
\end{tikzcd}
batch 6 · p. 111 — read it beside the facsimile22 / 49
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\begin{tikzcd}
  D_J \arrow[r, "f_x"] \arrow[d, no head, "\wr"'] & D_{d,\delta} \arrow[d, no head, "\wr"] \\
  {\widetilde{D}_d \wedge_{\mathfrak{S}_d} H(J)} & {D^{!}_d \wedge_{\mathfrak{S}_d} \mathfrak{P}_\delta(I_d)}
\end{tikzcd}
batch 6 · p. 111 — read it beside the facsimile23 / 49
LaTeX source
\begin{tikzcd}
  D_J \arrow[r] \arrow[d] & D_{J'} \arrow[d, "f_x"] \\
  D_{d,\delta} \arrow[r] & D_\delta
\end{tikzcd}
batch 6 · p. 112 — read it beside the facsimile24 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=tiny]
  & D_{d,d'} \arrow[r] \arrow[dr] & D_d \\
  D_{d,d',d''} \arrow[ur] \arrow[dr] & & D_{d'} \\
  & D_{d',d''} \arrow[ur] \arrow[r] & D_{d''}
\end{tikzcd}
batch 6 · p. 113 — read it beside the facsimile25 / 49
LaTeX source
\begin{tikzcd}
  & D_{**} \arrow[dl, "s"'] \arrow[dr, "b"] & \\
  D_{*} & & D_{*}
\end{tikzcd}
batch 6 · p. 116 — read it beside the facsimile26 / 49
LaTeX source
\begin{tikzcd}
  D^{!}_{d,d'} \arrow[r] \arrow[d, "\mathrm{can}"'] & D^{!}_{d'} \arrow[d, "\mathrm{can}"] \\
  D_{d,d'} \arrow[r, "b"'] & D_{d'}
\end{tikzcd}
batch 6 · p. 116 — read it beside the facsimile27 / 49
LaTeX source
\begin{tikzcd}
  D_{d,d',d''} \arrow[r] \arrow[d] & D_{d',d''} \arrow[d] \\
  D_{d,d'} \arrow[r] & D_{d'}
\end{tikzcd}
batch 6 · p. 117 — read it beside the facsimile28 / 49
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\begin{tikzcd}
  D_{d,d',d''} \arrow[r] \arrow[d, "\text{tautol.}"'] & D_{d',d''} \arrow[d, "\text{« but »}"] \\
  D_{d,d''} \arrow[r, "\text{« but »}"'] & D_{d''}
\end{tikzcd}
batch 6 · p. 118 — read it beside the facsimile29 / 49
LaTeX source
\begin{tikzcd}
  D_{d,0} \arrow[d, no head, "\wr"'] \arrow[dr] & \\
  D_d & D_0 \overset{\text{déf}}{=} X
\end{tikzcd}
batch 6 · p. 118 — read it beside the facsimile30 / 49
LaTeX source
\begin{tikzcd}
  D_{d,d'} \arrow[r, "b"] \arrow[d, "s"'] & D_{d'} \arrow[d] \\
  D_d \arrow[r] & X
\end{tikzcd}
batch 7 · p. 122 — read it beside the facsimile31 / 49
LaTeX source
\begin{tikzcd}[column sep=small]
  & D_{d,d'} \arrow[dl, "\text{rev. ét.}"'] \arrow[dr, "\text{imm. loc.}"] & \\
  D_d & & D_{d'}
\end{tikzcd}
batch 7 · p. 123 — read it beside the facsimile32 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  (D^{!}_{d'})^{(I_d)}_{D^{!}_d} \simeq D^{!}_{d,d'} \arrow[d] \arrow[rr, dashed] \arrow[dr, "\mathfrak{S}_{d}"] & & D^{!}_{d'} \arrow[dd, "\mathfrak{S}_{d'}"] \\
  D^{!}_d \arrow[dr, "\mathfrak{S}_d"'] & D_{d,d'} \arrow[d] \arrow[dr] & \\
  & D_d & D_{d'}
\end{tikzcd}
batch 7 · p. 125 — read it beside the facsimile33 / 49
LaTeX source
\begin{tikzcd}[column sep=small]
  & D_{d,d',d''} \arrow[dl] \arrow[d] \arrow[dr] & \\
  D_d & D_{d'} & D_{d''}
\end{tikzcd}
batch 7 · p. 125 — read it beside the facsimile34 / 49
LaTeX source
\begin{tikzcd}[column sep=small]
  & D_{d,d',d''} \arrow[dl] \arrow[d] \arrow[dr] & \\
  D_{d,d'} & D_{d',d''} & D_{d,d''}
\end{tikzcd}
batch 7 · p. 125 — read it beside the facsimile35 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  T(d,d',d'')_d \arrow[r] \arrow[rr, bend left=20] & T(d,d',d'')_{d'} \arrow[r] & T(d,d',d'')_{d''} \\
  G(d,d',d'')_d \arrow[r] \arrow[rr, bend left=20] & G(d,d',d'')_{d'} \arrow[r] & G(d,d',d'')_{d''} \\
  P(d,d',d'')_d \arrow[r] \arrow[rr, bend left=20] & P(d,d',d'')_{d'} \arrow[r] & P(d,d',d'')_{d''}
\end{tikzcd}
batch 7 · p. 128 — read it beside the facsimile36 / 49
LaTeX source
\begin{tikzcd}[column sep=small]
  \widetilde{\Pi}_{d_0 \dots d_r} \overset{\text{déf}}{=} \Pi_1 P^{*}_{d_0,\dots,d_r} \arrow[r] \arrow[d] & \Pi_1 P^{*}_{d_0} \bigl(\overset{\text{déf}}{=} \widetilde{\Pi}_{d_0}\bigr) \arrow[d] \\
  \Pi_{d_0 \dots d_r} = \Pi_1 D^{*}_{d_0,\dots,d_r} \arrow[r] & \Pi D^{*}_{d_0} \bigl(\overset{\text{déf}}{=} \Pi_{d_0}\bigr)
\end{tikzcd}
batch 7 · p. 131 — read it beside the facsimile37 / 49
LaTeX source
\begin{tikzcd}
  \widetilde{\Pi}_{\Delta_{r'}} \arrow[r] \arrow[d] & \widetilde{\Pi}_{\Delta_r} \arrow[d] \\
  \Pi_{\Delta_{r'}} \arrow[r] & \Pi_{\Delta_r}
\end{tikzcd}
batch 7 · p. 135 — read it beside the facsimile38 / 49
LaTeX source
\begin{tikzcd}
  D_{d_0,\dots,d_r} \arrow[r] \arrow[d] & D_{d'_0 \dots d'_{r'}} \arrow[d] \\
  D_{d_0,d'_0} \arrow[r] & D^{!}_{d'_0}
\end{tikzcd}
batch 7 · p. 139 — read it beside the facsimile39 / 49
LaTeX source
\begin{tikzcd}
  \Pi_1 P_{D''^{*}} \arrow[r, "r_{D'',D'}"] \arrow[d, "i_{D''}"'] & \Pi_1 P_{D'^{*}} \arrow[d, "i_{D'}"] \\
  \Pi_1 P_{D''} \arrow[r] & \Pi_1 P_{D'}
\end{tikzcd}
batch 8 · p. 152 — read it beside the facsimile40 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
 & D_{d,d'} \arrow[dl] \arrow[dr] & \\
D_d \arrow[dr] & & D_{d'} \arrow[dl] \\
 & D_0=X &
\end{tikzcd}
batch 8 · p. 153 — read it beside the facsimile41 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
 & D_{d,d'}^\Sigma \arrow[dl] \arrow[dr] & \\
D_d^\Sigma & & D_{d'}^\Sigma
\end{tikzcd}
batch 8 · p. 155 — read it beside the facsimile42 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
 & \Pi_1(V^*_{\Theta,X}) \arrow[dl] \arrow[dr] & \\
\Pi_1 X^* & & \Pi_1 V_{\Theta,X}
\end{tikzcd}
batch 9 · p. 163 — read it beside the facsimile43 / 49
LaTeX source
\begin{tikzcd}
 & \mathbb{P} \arrow[d, hook] \\
\mathbb{D}^* \arrow[r, hook] \arrow[d, hook] & \mathbb{D} \arrow[d, dashed] \\
\mathbb{C}^* \arrow[r, dashed] & \mathbb{C}
\end{tikzcd}
batch 9 · p. 167 — read it beside the facsimile44 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\mathcal{V}^*_{D_{d_*},D'_{d''_*}} \arrow[r, hook] & \mathcal{V}_{D'_{d_*},D_{d''_*}} \\
\mathcal{V}^{d'_*}_{d_*,d''_*} \arrow[u] \arrow[r] & \mathcal{V}^*_{D'_d,D''_d} \arrow[u, hook]
\end{tikzcd}
batch 9 · p. 169 — read it beside the facsimile45 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
 & \mathbb{D}^*\times\mathbb{C}^* \arrow[dl] \arrow[dr] & \\
\mathbb{C}^*\times\mathbb{C}^* \arrow[dr, dashed] & \text{loc.} & \mathbb{D}\times\mathbb{C}^* \arrow[dl, dashed] \\
 & U_1 & \\
 & \mathbb{C}^*\times\mathbb{D}^* \arrow[dl] \arrow[dr] & \\
\mathbb{C}^*\times\mathbb{C}^* \arrow[dr, dashed] & \text{loc.} & \mathbb{C}^*\times\mathbb{D} \arrow[dl, dashed] \\
 & U_2 &
\end{tikzcd}
batch 9 · p. 170 — read it beside the facsimile46 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
 & \mathbb{C}^*\times\mathbb{D}^* \arrow[dl] \arrow[dr] & & \mathbb{D}^*\times\mathbb{C}^* \arrow[dl] \arrow[dr] & \\
\mathbb{C}^*\times\mathbb{D} \arrow[drr, dashed] & & \mathbb{C}^*\times\mathbb{C}^* & & \mathbb{D}\times\mathbb{C}^* \arrow[dll, dashed] \\
 & & U=\mathbb{C}^2\setminus\{\mathbb{P}\} & &
\end{tikzcd}
batch 9 · p. 170 — read it beside the facsimile47 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\mathbb{C}^*\times\mathbb{C}^* & \mathbb{D}^*\times\mathbb{C}^* \arrow[l] \arrow[r] & \mathbb{D}\times\mathbb{C}^* \\
\mathbb{C}^*\times\mathbb{D}^* \arrow[u, no head] \arrow[d] & \mathbb{D}^*\times\mathbb{D}^* \arrow[l] \arrow[r] \arrow[u] \arrow[d] & \mathbb{D}\times\mathbb{D}^* \arrow[u] \arrow[d, no head] \\
\mathbb{C}^*\times\mathbb{D} & \mathbb{D}^*\times\mathbb{D} \arrow[l] \arrow[r] & \mathbb{D}\times\mathbb{D}
\end{tikzcd}
batch 9 · p. 179 — read it beside the facsimile48 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
 & \mathbb{D}^*_\infty \arrow[dl] \arrow[dr] & \\
\mathbb{D}_\infty & & {\mathbb{C}=\mathbb{P}^1_{\mathbb{C}}\setminus\{\infty\}=X^*}
\end{tikzcd}
batch 9 · p. 179 — read it beside the facsimile49 / 49
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
 & \mathbb{Z} \arrow[dl] \arrow[dr] & \\
\{1\} & & \{1\}
\end{tikzcd}