Cote n° 83 · pages 20–199 · 14 commutative diagrams · [Icosaèdres, bi-icosaèdres et algèbres d'Azumaya de rang 4] : notes manuscrites (1982-1983, 1986, s.d.).
Inventory dating : 1982-1986
Édition de démonstration

batch 1 · p. 20 — read it beside the facsimile1 / 14
LaTeX source
\begin{tikzcd}
\widetilde{\mathbb{Z}} \arrow[r, "\varepsilon"] \arrow[d, "u_0"'] & \mathbb{Z} \arrow[d, "u"] \\
T_0 \arrow[r, "c_0"] & T_H
\end{tikzcd}
batch 2 · p. 24 — read it beside the facsimile2 / 14
LaTeX source
\begin{tikzcd}
\tilde Z \arrow[r, "{\delta_{\tilde Z} : \tilde\lambda \mapsto \dot{\tilde\lambda}}"] \arrow[rr, bend right=40, "{\tilde\lambda \mapsto \tilde\lambda^2}"'] & Z \arrow[r, "{\tilde\delta | Z}"] & \tilde Z
\end{tikzcd}
batch 2 · p. 26 — read it beside the facsimile3 / 14
LaTeX source
\begin{tikzcd}[column sep=large]
U \arrow[r, hook, "Z"] \arrow[d, hook, "\mu_2"'] & B'' \arrow[r, hook] \arrow[d, hook, "\mu_2"'] & G_0^+ \arrow[d, hook, "\mu_2"'] \\
\tilde U \arrow[r, hook, "Z"] \arrow[d, hook, "Z"'] & \tilde B'' \arrow[r, hook] \arrow[d, hook, "Z"'] & G_0 \arrow[d, hook, "Z"'] \\
B' \arrow[r, hook, "Z"] & B \arrow[r, hook] & G
\end{tikzcd}
batch 4 · p. 71 — read it beside the facsimile4 / 14
LaTeX source
\begin{tikzcd}[column sep=large]
{[E^*/k^* \simeq \mathbb{P}(E)(k)]} \arrow[r, "\sim"] & C^*/k^* \\
E^* \arrow[u] \arrow[r, "\varphi^e"] & C^*(e)\subset C^* \arrow[u]
\end{tikzcd}
batch 7 · p. 127 — read it beside the facsimile5 / 14
LaTeX source
\begin{tikzcd}
 & P & \\
H \arrow[ur, "i_0"] & & H' \arrow[ul, "j_0"']
\end{tikzcd}
batch 7 · p. 127 — read it beside the facsimile6 / 14
LaTeX source
\begin{tikzcd}
 & P & \\
 & B \arrow[u] & \\
H \arrow[ur] \arrow[uur, "i_0"] & & H' \arrow[ul] \arrow[uul, "j_0"']
\end{tikzcd}
batch 7 · p. 129 — read it beside the facsimile7 / 14
LaTeX source
\begin{tikzcd}
 & A & \\
H \arrow[ur, "i"] & & H' \arrow[ul, "j"']
\end{tikzcd}
batch 7 · p. 129 — read it beside the facsimile8 / 14
LaTeX source
\begin{tikzcd}
 & A & \\
 & P \arrow[u, "f"] & \\
 & B \arrow[u] & \\
H \arrow[ur] & & H' \arrow[ul] \\
 & k \arrow[ul, "\varepsilon_H"] \arrow[ur, "\varepsilon_{H'}"'] &
\end{tikzcd}
batch 7 · p. 132 — read it beside the facsimile9 / 14
LaTeX source
\begin{tikzcd}
\underline{Q}_P \arrow[r, "\alpha"] \arrow[dr, "\delta"'] & \underline{Q}_B \arrow[r, "\beta"] & \underline{\Psi}_B \arrow[r, "\gamma"] & \underline{\Phi}_B \arrow[dll] \\
 & \underline{L}_P & &
\end{tikzcd}
batch 7 · p. 135 — read it beside the facsimile10 / 14
LaTeX source
\begin{tikzcd}[column sep=small, row sep=large, nodes={font=\scriptsize}]
AZ_P \arrow[r] \arrow[drr, "\alpha\mapsto\operatorname{Tr}_\alpha"'] & \underline{Q}_P \arrow[r] \arrow[dr, dashed] & \underline{Q}_B \arrow[r] & \underline{\Psi}_B \arrow[r] & \underline{\Phi}_B \arrow[dll, "{\varphi\mapsto(x\otimes y\mapsto\varphi(x,y))}"] \\
 & & \underline{L}_P & &
\end{tikzcd}
batch 8 · p. 159 — read it beside the facsimile11 / 14
LaTeX source
\begin{tikzcd}[column sep=large]
  \bigotimes E_i^0 \arrow[d, "i"'] \arrow[dr, "{(-2)^{n-1}\,\mathrm{can}}"] & \\
  \mathop{\ast}(E_i, \sigma_i) \arrow[r, "\tau"] \arrow[dr, "{2^{n-1}J}"'] & \bigotimes E_i \arrow[d, "\mathrm{can}"] \\
  & \bigotimes E_i/E_i^0
\end{tikzcd}
batch 9 · p. 169 — read it beside the facsimile12 / 14
LaTeX source
\begin{tikzcd}[column sep=large]
A_1 \times A_2 \arrow[r, "\ast"] \arrow[d, "\pi_1 \times \pi_2"'] & A = A_1 \ast A_2 \arrow[d, "\pi_A"] \\
Q_1 \times Q_2 \arrow[r, "\otimes"] \arrow[d, "\delta_{A_1} \times \delta_{A_2}"'] & Q = Q_{A, \sigma_A} \arrow[d, "\delta_A"] \\
L_1^{\otimes 2} \times L_2^{\otimes 2} \arrow[r, "{\text{can}, \sim}"] & (L_1 L_2)^{\otimes 2}
\end{tikzcd}
batch 10 · p. 194 — read it beside the facsimile13 / 14
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  B & & \\
  A \arrow[u, no head] \arrow[r, no head, "\mathfrak{S}_2"] \arrow[d, no head, "\mathfrak{S}_3"'] & B \arrow[d, no head, "\mathfrak{S}_3"] & \\
  A^{\mathfrak{S}_3} \arrow[r, no head, "\mathfrak{S}_2"'] \arrow[d, no head] & B_0 \arrow[d, no head] & \\
  \mathbb{Z}[\Sigma, \Pi] \arrow[r, no head] & B_{00} &
\end{tikzcd}
batch 10 · p. 199 — read it beside the facsimile14 / 14
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  A \arrow[r] & B & \\
  A^{\mathfrak{S}_3^+} \arrow[u, "3"] \arrow[r, no head, "2"] & B_1 = B^{\mathfrak{S}_3^+} \arrow[u, "3"'] & \\
  A^{\mathfrak{S}_3} \arrow[u, "2"] \arrow[r, no head, "2"'] & B_0 \arrow[u, "2"'] & B^{\mathfrak{S}_3}
\end{tikzcd}