Cote n° 149 · pages 4–134 · 18 commutative diagrams · [Autour de La "Longue Marche" à travers la théorie de Galois, pages 1 à 67] : notes manuscrites (s.d.).
Inventory dating : s.d.
Édition de démonstration

batch 1 · p. 4 — read it beside the facsimile1 / 18
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
K_1 \arrow[r, no head] \arrow[dr, no head] & K' \arrow[dr, no head] & \\
 & \overline{K} \arrow[r, no head] & \overline{K}'
\end{tikzcd}
batch 1 · p. 9 — read it beside the facsimile2 / 18
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
(8)\qquad 1 \arrow[r] & \pi \arrow[r] & E \arrow[r] & \Gamma_{\overline{K}/K} \arrow[r] \arrow[d, hook] & 1 \\
 & & & \Gamma_{\overline{\mathbb{Q}}/\mathbb{Q}} &
\end{tikzcd}
batch 1 · p. 10 — read it beside the facsimile3 / 18
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
 & \operatorname{Spec}(K) = \eta \arrow[r] \arrow[d] & \eta_{\overline{\mathbb{Q}}} \arrow[r, no head] \arrow[d, no head] & \bar\eta = \operatorname{Spec}(\overline{K}) \\
 & U_i \arrow[r, no head] \arrow[d, no head] & U_{i,\overline{\mathbb{Q}}} = \overline{U}_i \arrow[d, no head] & \\
\mathbb{Q} \arrow[r, no head] & k \arrow[r, no head] & \overline{\mathbb{Q}} &
\end{tikzcd}
batch 1 · p. 16 — read it beside the facsimile4 / 18
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
(15)\qquad 1 \arrow[r] & \pi \arrow[r] & \operatorname{Aut}(\pi) \arrow[r] & \operatorname{Autext}(\pi) \arrow[r] & 1 \\
 & & & \Gamma \arrow[u, "\varphi"'] &
\end{tikzcd}
batch 2 · p. 21 — read it beside the facsimile5 / 18
LaTeX source
\begin{tikzcd}
p f^{*}(\overline{\eta}') \arrow[r, "p(\alpha)", "\sim"'] \arrow[d, "\wr"'] & p g^{*}(\overline{\eta}') \arrow[d, "\wr"] \\
p'(\overline{\eta}') \arrow[r, "\sim"'] & p'(\overline{\eta}')
\end{tikzcd}
batch 2 · p. 21 — read it beside the facsimile6 / 18
LaTeX source
\begin{tikzcd}
\Pi_{K'} \arrow[dr, "p'"'] & \overset{f^{*}}{\underset{g^{*}}{\rightrightarrows}} & \Pi_{K} \arrow[dl, "p"] \\
& \Pi_{\mathbb{Q}} &
\end{tikzcd}
batch 3 · p. 57 — read it beside the facsimile7 / 18
LaTeX source
\begin{tikzcd}
X \arrow[r, no head] & \overline{X} \arrow[r, no head] & X' \\
U \arrow[r, no head] \arrow[u, no head, "\cup" description] \arrow[d, no head]
 & \overline{U} \arrow[r, no head] \arrow[u, no head, "\cup" description] \arrow[d, no head]
 & \widetilde{U} \arrow[u, no head, "\cup" description] \\
K \arrow[r, no head] & \overline{K} &
\end{tikzcd}
batch 4 · p. 63 — read it beside the facsimile8 / 18
LaTeX source
\begin{tikzcd}
\pi \arrow[d] \arrow[r, no head, "\sim"] & \pi \arrow[d] \\
\mathcal{E}_{\mathcal{U}_S} \arrow[d] & \mathcal{E}_{\mathcal{U}_K} \arrow[l] \arrow[d] \\
\mathcal{E}_S & \mathcal{E}_K \arrow[l, "\text{surj}"']
\end{tikzcd}
batch 4 · p. 72 — read it beside the facsimile9 / 18
LaTeX source
\begin{tikzcd}[column sep=small]
\mathcal{U}_S \arrow[d, no head] & \mathcal{U}_{\mathcal{O}_x} \arrow[l, no head] \arrow[d, no head] & \mathcal{U}_K \arrow[l, no head] \arrow[d, no head] & \mathcal{U}_{\overline{K}} \arrow[l, no head] \arrow[d, no head] & \widetilde{\mathcal{U}}_S \arrow[l, no head] \\
S & \mathcal{O}_x \arrow[l, no head] & K \arrow[l, no head] & \overline{K} \arrow[l, no head] &
\end{tikzcd}
batch 4 · p. 72 — read it beside the facsimile10 / 18
LaTeX source
\begin{tikzcd}
\mathcal{E}_{\mathcal{U}_S} \arrow[d] & \mathcal{E}_{\mathcal{U}_{\mathcal{O}_x}} \arrow[l] \arrow[d] & \mathcal{E}_{\mathcal{U}_K} \arrow[l] \arrow[d] \\
\mathcal{E}_S & \mathcal{E}_{\mathcal{O}_x} \arrow[l] & \mathcal{E}_K \arrow[l] \arrow[ul, dashed, "\varphi_x"']
\end{tikzcd}
batch 4 · p. 73 — read it beside the facsimile11 / 18
LaTeX source
\begin{tikzcd}
\mathcal{E}_{\mathcal{U}} \arrow[d, "\text{surj}"'] & \mathcal{E}_{\mathcal{U}_K} \arrow[l, "\text{surj}"'] \arrow[d, "\text{surj}"] \\
\mathcal{E}_S & \mathcal{E}_K = \operatorname{Gal}(\overline{K}/K) \arrow[l, "\text{surj}"]
\end{tikzcd}
batch 5 · p. 87 — read it beside the facsimile12 / 18
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
 & & 1 \arrow[d] & 1 \arrow[d] & \\
 & & I \arrow[r, "\simeq"] \arrow[d] & I_{s'} \simeq T \arrow[d] & \\
1 \arrow[r] & \pi \arrow[r] \arrow[d, no head] & \mathcal{E}_{U_{\tilde{K}}} \arrow[r] \arrow[d] & \mathcal{E}_{\tilde{K}} \arrow[r] \arrow[d] & 1 \\
1 \arrow[r] & \pi \arrow[r] & \mathcal{E}_{U_{\tilde{\mathcal{O}}}} \arrow[r] \arrow[d] & \mathcal{E}_{\tilde{\mathcal{O}}} \arrow[r] \arrow[d] & 1 \\
 & & 1 & 1 &
\end{tikzcd}
batch 5 · p. 88 — read it beside the facsimile13 / 18
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
U_s \arrow[r] \arrow[d] & U_{\tilde{\mathcal{O}}} \arrow[d] \\
s \arrow[r] & \operatorname{Spec} \tilde{\mathcal{O}}
\end{tikzcd}
batch 6 · p. 109 — read it beside the facsimile14 / 18
LaTeX source
\begin{tikzcd}
X \arrow[d] & X_T \arrow[l] \arrow[d] & \\
Y & T \arrow[l] & T \arrow[ul] \arrow[l, no head, "="]
\end{tikzcd}
batch 6 · p. 111 — read it beside the facsimile15 / 18
LaTeX source
\begin{tikzcd}
X \arrow[d] & X_{\tilde{Y}} \arrow[l] \arrow[d] & \tilde{X} \arrow[l] & Z \arrow[l] \\
Y' \arrow[d] & \tilde{Y} \arrow[l] & & \\
Y & & &
\end{tikzcd}
batch 7 · p. 133 — read it beside the facsimile16 / 18
LaTeX source
\begin{tikzcd}
U_J \arrow[r] \arrow[d, "i"'] & U \arrow[d] \\
X_J \arrow[r] & \operatorname{Spec} K = \xi \\
D_J \arrow[u, "\text{équiv.\ d'homotopie}"']
\end{tikzcd}
batch 7 · p. 133 — read it beside the facsimile17 / 18
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
 & \pi_2(D_J) & T^{J} & \mathcal{E}_{U_J} & \mathcal{E}_{D_J} & \\
\cdots \arrow[r] & \pi_2(X_J) \arrow[u, no head, "\parallel"'] \arrow[r] \arrow[d] & \pi_1(\overline{\mathbb{G}}_m^{\,J}) \arrow[u, no head, "\wr"'] \arrow[r] \arrow[d] & \pi_1(U_J) \arrow[u, no head, "\wr"'] \arrow[r] \arrow[d] & \pi_1(X_J) \arrow[u, no head, "\wr"'] \arrow[r] \arrow[d] & 1 \\
\cdots \arrow[r] & \pi_2(\xi) \arrow[r] \arrow[d, no head, "\parallel"'] & \pi_1(U_{\overline{\xi}}) \arrow[r] \arrow[d, no head, "\wr"'] & \pi_1(U) \arrow[r] \arrow[d, no head, "\wr"'] & \pi_1(\xi) \arrow[r] \arrow[d, no head, "\wr"'] & 1 \\
 & 0 & \pi_{U/K} & \mathcal{E}_U & \mathcal{E}_K &
\end{tikzcd}
batch 7 · p. 134 — read it beside the facsimile18 / 18
LaTeX source
\begin{tikzcd}[column sep=small]
1 \arrow[r] & T^{J} \arrow[r] \arrow[d] & \mathcal{E}_{U_{J,\alpha}}^{\overline{L}} \arrow[r] \arrow[d] & \mathcal{E}_{D_{J,\alpha}}^{\widetilde{D}_{J,\alpha}} \arrow[r] \arrow[d] & 1 \\
1 \arrow[r] & \pi_{U/K}^{\overline{L}} \arrow[r] & \mathcal{E}_U^{\overline{L}} \arrow[r] & \mathcal{E}_K^{\overline{K}} \arrow[r] & 1
\end{tikzcd}