Cote n° 77 · pages 28–156 · 9 commutative diagrams · Quadriques affines, extensions quadratiques : notes manuscrites (s.d.).
Inventory dating : [à partir de 1977]
Édition de démonstration

batch 2 · p. 28 — read it beside the facsimile1 / 9
LaTeX source
\begin{tikzcd}
\check{\mathbb{V}}\sum_{1 \le i \le n} L^{\otimes i} \arrow[r, "\varphi_n(\tau)"] & \check{\mathbb{V}}\sum_{1 \le i \le n} L^{\otimes i}\\
\check{\mathbb{V}}L^n \arrow[u, "\sigma_n"] \arrow[r, "(\mathrm{trans}\,\tau)^n"] & \check{\mathbb{V}}(L^n) \arrow[u, "\sigma_n"']
\end{tikzcd}
batch 2 · p. 36 — read it beside the facsimile2 / 9
LaTeX source
\begin{tikzcd}[column sep=small, row sep=normal, nodes={font=\small}]
\mathrm{Sym}^n(\check{V}) \arrow[r, hook] & \mathrm{Sym}^*(\check{V}) = \mathrm{Algaff}\,\check{\mathbb{V}}(V) \arrow[r] & \mathrm{Sym}^*(\check{V})/(e_V - 1) \arrow[d, no head, "\Vert" description]\\
L^{\otimes(-n)} \otimes \underline{\mathrm{Sym}}^n(V) \arrow[u, "{\mathrm{Sym}^n(\alpha) = \alpha_n}", "\wr"'] \arrow[d, "{\mathrm{Sym}^n(\alpha) = \alpha_n}"', "\wr"] & & \mathrm{Algaff}(F)\\
\underline{\mathrm{Sym}}^n(\check{V}) \arrow[r, "J_n"] & \mathrm{Algaff}(F) &
\end{tikzcd}
batch 2 · p. 37 — read it beside the facsimile3 / 9
LaTeX source
\begin{tikzcd}[column sep=normal, row sep=large]
L^{\otimes -n} \otimes \underline{\mathrm{Sym}}^n(V) \arrow[r, "\alpha_n", "\sim"'] \arrow[d, "i_n"', "{\mathrm{id}_{L^{\otimes(-n-1)}} \otimes \ldots}"] & \underline{\mathrm{Sym}}^n(\check{V}) \arrow[r, hook, "J_n"] \arrow[d, "{\text{mult. par } e_{\check{V}} = i'_1(1)}"] & \underline{\mathrm{Algaff}}(F) \arrow[d, no head, "\Vert" description]\\
L^{\otimes(-n-1)} \otimes \underline{\mathrm{Sym}}^{n+1}(V) \arrow[r, "\sim", "\alpha_{n+1}"'] & \underline{\mathrm{Sym}}^{n+1}(\check{V}) \arrow[r, hook, "J_{n+1}"] & \mathrm{Algaff}(F)
\end{tikzcd}
batch 2 · p. 38 — read it beside the facsimile4 / 9
LaTeX source
\begin{tikzcd}[column sep=small, row sep=normal, nodes={font=\small}]
\underline{\mathrm{Div}}^{+n}_{F/S} \arrow[r, "\sim"] & \underline{\mathrm{Splittings}}\ \text{de}\ \bigl(0 \to \underline{\mathrm{Sym}}^{n-1}(\check{V}) \to \underline{\mathrm{Sym}}^n(\check{V}) \to L^{\otimes -n} \to 0\bigr)\\
\Sigma^n(F/S) \arrow[u, "\wr"] & \underline{\mathrm{splittings}}\ \text{de}\ L^{\otimes \ldots}\ \ldots \arrow[u, no head, "\wr" description]
\end{tikzcd}
batch 2 · p. 40 — read it beside the facsimile5 / 9
LaTeX source
\begin{tikzcd}
\underline{\mathrm{Algaff}}(F) \arrow[r] & C_n\\
\underline{\mathrm{Sym}}^*(B)/(e_B - 1) \arrow[u, "\wr"']
\end{tikzcd}
batch 6 · p. 106 — read it beside the facsimile6 / 9
LaTeX source
\begin{tikzcd}
  & X \arrow[dl, hook'] \arrow[dr, hook, "i"] & \\
  X^{\Omega} \arrow[rr, "\sim"] & & \hat{\Sigma}
\end{tikzcd}
batch 8 · p. 154 — read it beside the facsimile7 / 9
LaTeX source
\begin{tikzcd}[column sep=large]
\underline{O}_D(q) \arrow[r] \arrow[rr, bend right=30, "\det_E"'] & \underline{O}(q_Q) \arrow[r, "\det_Q"] & \mathbb{G}_m
\end{tikzcd}
batch 8 · p. 154 — read it beside the facsimile8 / 9
LaTeX source
\begin{tikzcd}[column sep=small, row sep=normal, nodes={font=\small}]
1 \arrow[r] & \underline{O}_D(q)^{+} \arrow[r] & \underline{O}_D(q) \arrow[r] & \prod_{1\le i\le\nu}\underline{Gl}(R_i)\times\underline{O}(q_Q) \arrow[r] & 1\\
1 \arrow[r] & \underline{SO}_D(q)^{+} \arrow[r] \arrow[u, "\wr"] & \underline{SO}_D(q) \arrow[r] \arrow[u, hook] & \prod_{1\le i\le\nu}\underline{Gl}(R_i)\times\underline{SO}(q_Q) \arrow[r] \arrow[u, hook] & 1
\end{tikzcd}
batch 8 · p. 156 — read it beside the facsimile9 / 9
LaTeX source
\begin{tikzcd}[column sep=small, nodes={font=\small}]
1 \arrow[r] & \underline{O}_D(q)^{+} \arrow[r] & \underline{O}_D(q) \arrow[r] & \prod_{1\le i\le\nu}\underline{Gl}(R_i)\times\underline{O}(q_Q) \arrow[r] & 1\\
1 \arrow[r] & \underline{SO}_D(q)^{+} \arrow[r] \arrow[u, "\wr"] & \underline{SO}_D(q) \arrow[r] \arrow[u, hook] & \prod_{1\le i\le\nu}\underline{Gl}(R_i)\times\underline{SO}(q_Q) \arrow[r] & 1
\end{tikzcd}