Cote n° 138 · pages 4–128 · 25 commutative diagrams · Cartes. Etude arithmétique (1976, 77 ?) : bon de commande (s.d.), notes manuscrites (s.d.).
Inventory dating : [vers 1976-1978]
Édition de démonstration

batch 1 · p. 4 — read it beside the facsimile1 / 25
LaTeX source
\begin{tikzcd}
  1 \arrow[r] & \mathfrak{G} \arrow[r] \arrow[d, no head, "\parallel" description] & \mathcal{G} \arrow[r] & \Gamma \\
  1 \arrow[r] & \mathfrak{G} \arrow[r] & \mathcal{G}_1 \arrow[r] \arrow[u, hook, "\mathrm{cart}"'] & \Gamma_1 \arrow[u, hook]
\end{tikzcd}
batch 1 · p. 4 — read it beside the facsimile2 / 25
LaTeX source
\begin{tikzcd}
  1 \arrow[r] & \mathfrak{G} \arrow[r] & \mathcal{G} \arrow[r] & \Gamma \arrow[r, "!"] \arrow[l, bend left=40] & 1
\end{tikzcd}
batch 1 · p. 5 — read it beside the facsimile3 / 25
LaTeX source
\begin{tikzcd}
  \mathcal{G} \arrow[r] & \Gamma \\
  & \Gamma_1 \arrow[u, hook] \arrow[ul, dashed]
\end{tikzcd}
batch 1 · p. 6 — read it beside the facsimile4 / 25
LaTeX source
\begin{tikzcd}
  1 \arrow[r] & G \arrow[r] & \mathcal{G}' \arrow[r] & \mathcal{G} \arrow[r, dashed] & \Gamma
\end{tikzcd}
batch 1 · p. 8 — read it beside the facsimile5 / 25
LaTeX source
\begin{tikzcd}
  \mathcal{G}' \arrow[r] & \Gamma \arrow[l, bend left=40]
\end{tikzcd}
batch 1 · p. 8 — read it beside the facsimile6 / 25
LaTeX source
\begin{tikzcd}
  \mathcal{G}' \arrow[r] & \Gamma \\
  & \Gamma_1 \arrow[u, hook] \arrow[ul]
\end{tikzcd}
batch 1 · p. 10 — read it beside the facsimile7 / 25
LaTeX source
\begin{tikzcd}
  1 \arrow[r] & \mathfrak{G}' \arrow[r] & \mathcal{G}' \arrow[r] & \Gamma \arrow[r] & 1 \\
  & & & \Gamma_i \arrow[u, hook] \arrow[ul]
\end{tikzcd}
batch 1 · p. 12 — read it beside the facsimile8 / 25
LaTeX source
\begin{tikzcd}
  Z \arrow[r] & \Gamma \\
  & \Gamma_i \arrow[u, hook] \arrow[ul]
\end{tikzcd}
batch 1 · p. 18 — read it beside the facsimile9 / 25
LaTeX source
\begin{tikzcd}
  X' \simeq \mathbb{P}^1_{\mathbb{Q}} \arrow[r, no head] \arrow[d, "\mu_{n\,\mathbb{Q}}"'] & \bar{X}' \arrow[d, no head] \\
  X = \mathbb{P}^1_{\mathbb{Q}} \arrow[r, no head] \arrow[d, no head] & \bar{X} \arrow[d, no head] \\
  \mathbb{Q} \arrow[r, no head, "\Gamma"'] & \bar{\mathbb{Q}}
\end{tikzcd}
batch 1 · p. 18 — read it beside the facsimile10 / 25
LaTeX source
\begin{tikzcd}
  1 \arrow[r] & \mu_n(\bar{\mathbb{Q}}) \arrow[r] & \mathcal{E}_n \arrow[r] & \Gamma \arrow[r] \arrow[l, bend left=40] & 1
\end{tikzcd}
batch 1 · p. 19 — read it beside the facsimile11 / 25
LaTeX source
\begin{tikzcd}
  D \subset \mathbb{G}_m \arrow[d, "\text{fini}"'] \\
  \mathbb{Q}
\end{tikzcd}
batch 1 · p. 19 — read it beside the facsimile12 / 25
LaTeX source
\begin{tikzcd}
  \Gamma \arrow[r] \arrow[dr] & \mathrm{Aff}(T_\infty(\mathcal{U})) \arrow[d] \\
  & \mathrm{Aut}(T_\infty(\mathcal{U}))
\end{tikzcd}
batch 1 · p. 19 — read it beside the facsimile13 / 25
LaTeX source
\begin{tikzcd}
  \Gamma \arrow[r] \arrow[dr] & \mathrm{Aff}(n, \hat{\mathbb{Z}}) \arrow[d] \\
  & \hat{\mathbb{Z}}^{*} \cdot \hat{\mathbb{Z}}^{n}
\end{tikzcd}
batch 2 · p. 22 — read it beside the facsimile14 / 25
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
1 \arrow[r] & \mu_\nu \arrow[r] & \Gamma'_\nu \arrow[r] & (\mathbb{Z}/\nu\mathbb{Z})^{*} \arrow[r] & 1 \\
1 \arrow[r] & \mu_\nu \arrow[r] \arrow[u, no head, "\Vert" description] & \Gamma' \arrow[r] \arrow[u] & (\mathbb{Z}/6n\mathbb{Z})^{*} \arrow[r] \arrow[u] & 1
\end{tikzcd}
batch 2 · p. 32 — read it beside the facsimile15 / 25
LaTeX source
\begin{tikzcd}[column sep=large]
\widetilde{C}_n/\mu_{3n} \arrow[r] \arrow[d, "\wr"'] & \widetilde{C}_1/\mu_n \arrow[d, "\wr"] \\
E_n(\{\alpha, \overline{\alpha}\}) \arrow[r] & E_1(\{\alpha, \overline{\alpha}\})
\end{tikzcd}
batch 3 · p. 50 — read it beside the facsimile16 / 25
LaTeX source
\begin{tikzcd}
  X \arrow[r, "2"] \arrow[dr, bend right=20, "f_n"'] & X' \arrow[r, "?"] & X' \\
  & X \arrow[ur, "2"'] &
\end{tikzcd}
batch 3 · p. 53 — read it beside the facsimile17 / 25
LaTeX source
\begin{tikzcd}
  \widetilde{X}_2 \arrow[d] & \cdot \arrow[l] \\
  X_4 & X_8 \arrow[l]
\end{tikzcd}
batch 4 · p. 67 — read it beside the facsimile18 / 25
LaTeX source
\begin{tikzcd}
  X \arrow[d] & X' \arrow[l] \arrow[d] \\
  Y & Y' \arrow[l]
\end{tikzcd}
batch 4 · p. 76 — read it beside the facsimile19 / 25
LaTeX source
\begin{tikzcd}
  & E \arrow[dl, "\pi_{01}"'] \arrow[d, "\pi_{02}"] \arrow[dr, "\pi_{12}"] & \\
  R & R & R
\end{tikzcd}
batch 4 · p. 76 — read it beside the facsimile20 / 25
LaTeX source
\begin{tikzcd}
  & E^{+} \arrow[dl, "\pi_{01}^{+}"'] \arrow[d, "\pi_{02}^{+}"] \arrow[dr, "\pi_{12}^{+}"] & \\
  R & R & R \\
  & E^{-} \arrow[ul, "\pi_{01}^{-}"] \arrow[u, "\pi_{02}^{-}"'] \arrow[ur, "\pi_{12}^{-}"'] &
\end{tikzcd}
batch 5 · p. 89 — read it beside the facsimile21 / 25
LaTeX source
\begin{tikzcd}
  \widehat{L}_{\nu} \arrow[r, hook] \arrow[d] & \widehat{B}_{\nu} \arrow[r, "\widehat{\chi}_{\nu}^{0}"] \arrow[d] & (\mathbb{Z}^{*})^{\wedge} = \pm 1 \arrow[d] \\
  \widehat{L}_{\nu} \arrow[r] & A_{\nu} \arrow[r, "\chi_{\nu}"] & \mathbb{Z}^{*}
\end{tikzcd}
batch 5 · p. 89 — read it beside the facsimile22 / 25
LaTeX source
\begin{tikzcd}
  1 \arrow[r] & \widehat{\mathcal{T}}_{\nu}^{0} \arrow[r] \arrow[d, "\mathrm{can}"] & \widehat{\mathcal{T}}_{\nu} \arrow[r] \arrow[d] & \mathbb{Z}/2 \arrow[r] \arrow[d] & 1 \\
  1 \arrow[r] & \Gamma_{\nu}^{0} \arrow[r] & \Gamma_{\nu} \arrow[r] & \widehat{\mathbb{Z}}^{*} \arrow[r] & 1
\end{tikzcd}
batch 5 · p. 94 — read it beside the facsimile23 / 25
LaTeX source
\begin{tikzcd}
  \pi_{i} \arrow[r] & \pi \\
  I_{i} \arrow[u] \arrow[ur, "\alpha_{i}(\varphi)"'] &
\end{tikzcd}
batch 5 · p. 95 — read it beside the facsimile24 / 25
LaTeX source
\begin{tikzcd}
  \pi \arrow[r, "\beta(\varphi)"] & \widetilde{\pi} \\
  I_{i} \arrow[u, "\alpha_{i}(\varphi)"] \arrow[ur, "\alpha'_{i}(\varphi)"'] &
\end{tikzcd}
batch 7 · p. 128 — read it beside the facsimile25 / 25
LaTeX source
\begin{tikzcd}
X \arrow[rr, "f"', "\simeq"] \arrow[dr, "\varphi"'] & & X \arrow[dl, "\varphi'"] \\
& S &
\end{tikzcd}