Cote n° 36 · pages 14–82 · 12 diagrammes commutatifs · SGA 7 (ma part) : notes manuscrites (s.d.), tapuscrit annoté (s.d.).
Datation de l’inventaire : [vers 1967-1973]
Édition de démonstration

batch 1 · p. 14 — lire la page1 / 12
LaTeX source
\begin{tikzcd}
Y \arrow[rr, "i"] \arrow[dr, "f"'] & & X_S \arrow[dl, "g"] \\
& S &
\end{tikzcd}
batch 2 · p. 27 — lire la page2 / 12
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\begin{tikzcd}[column sep=small, row sep=small]
0 \arrow[r] & T \arrow[r] \arrow[d, no head, "\simeq"'] & G \arrow[r] & B \arrow[r] & 0 \\
 & D(M') & & & \\
0 \arrow[r] & T' \arrow[r] \arrow[d, no head, "\simeq"'] & G' \arrow[r] & B' \arrow[r] & 0 \\
 & D(M) & & &
\end{tikzcd}
batch 2 · p. 30 — lire la page3 / 12
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\begin{tikzcd}[column sep=small, row sep=small]
 & A & & & A' & \\
M \arrow[ur, "1"] \arrow[r] & G \arrow[u] & & M' \arrow[ur, "1"] \arrow[r] & G' \arrow[u] &
\end{tikzcd}
batch 2 · p. 32 — lire la page4 / 12
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\begin{tikzcd}[column sep=small]
\operatorname{Ext}^1(A \overset{L}{\otimes} A', \mathbb{G}_m) \arrow[r] \arrow[dr] &
\operatorname{Ext}^1({}_nA \overset{L}{\otimes} {}_nA', \mathbb{G}_m) \arrow[d] \\
 & \operatorname{Hom}({}_nA \otimes {}_nA', \mathbb{G}_m)
\end{tikzcd}
batch 2 · p. 39 — lire la page5 / 12
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\begin{tikzcd}[row sep=small]
\operatorname{Ext}^1(\underline{\operatorname{Alb}}_X, A) \arrow[r] \arrow[d, "\wr"] & H^1(X, A) \\
\operatorname{Ext}^1(A', \underline{\operatorname{Alb}}_X{}') \arrow[d, "\wr"] & \\
\operatorname{Ext}^1(A', \underline{\operatorname{Pic}}^{\tau}) &
\end{tikzcd}
batch 3 · p. 41 — lire la page6 / 12
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\begin{tikzcd}
f^{-1}(U) \arrow[r, hook, "i"] \arrow[d, "f"'] & X \arrow[d, "f"] \\
U \arrow[r, "j"'] \arrow[u, bend right=30, "g"'] & Y
\end{tikzcd}
batch 3 · p. 51 — lire la page7 / 12
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\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
0 \arrow[r] & \underline{\operatorname{Ext}}^1(A, G) \arrow[r, "i"] & R^1f_*(G_A) \arrow[r, "j"] \arrow[dl, "k"'] & \underline{\operatorname{Tors}}\,\underline{\operatorname{birig}}\,\underline{\operatorname{sym}}(A, A; G) \arrow[d, no head, "\Vert" description] \\
0 \arrow[r] & \underline{NS}(A) \arrow[rr, "j'"] & & \underline{\operatorname{Tors}}\,\underline{\operatorname{birig}}\,\underline{\operatorname{sym}}(A, A; G)
\end{tikzcd}
batch 3 · p. 53 — lire la page8 / 12
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\begin{tikzcd}[row sep=small]
A \arrow[r, no head] \arrow[d, "f"'] & A \times_S B \arrow[d, "f_B"] \\
S \arrow[r, no head] & B
\end{tikzcd}
batch 4 · p. 62 — lire la page9 / 12
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\begin{tikzcd}
X \arrow[d, "f"'] & X' \arrow[l, "h"'] \arrow[d, "f'"] \\
S & S' \arrow[l, "g"']
\end{tikzcd}
batch 4 · p. 64 — lire la page10 / 12
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\begin{tikzcd}[column sep=small, row sep=small]
H^1(X, \mu_n) \arrow[r, "\alpha"] \arrow[d] & {}_n\mathrm{Pic}(X) \arrow[d] & & \\
H^1(X_\eta, \mu_n)/(\mathbf{Z}/n\mathbf{Z}) \arrow[r, "\alpha_\eta"] \arrow[d] & {}_n\mathrm{Pic}(X_\eta) \arrow[r, "\beta_\eta"] \arrow[d] & {}_nP(K) \arrow[r, "\simeq"] \arrow[d] & {}_nP(\bar K)^I \arrow[dl, bend left=20] \\
H^1(X_{\bar\eta}, \mu_n) \arrow[r, "\alpha_{\bar\eta}"] & {}_n\mathrm{Pic}(X_{\bar\eta}) \arrow[r, "\beta_{\bar\eta}"] & {}_nP(\bar K) &
\end{tikzcd}
batch 5 · p. 82 — lire la page11 / 12
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\begin{tikzcd}[column sep=small, row sep=small]
 & 0 \arrow[d] & 0 \arrow[d] & 0 \arrow[d] & \\
0 \arrow[r] & \Phi \arrow[r] \arrow[d] & P^0 \arrow[r] \arrow[d] & Q^0 \arrow[r] \arrow[d] & 0 \\
0 \arrow[r] & E \arrow[r] \arrow[d] & P' \arrow[r] \arrow[d] & Q' \arrow[r] \arrow[d] & 0 \\
0 \arrow[r] & E/\Phi \arrow[r] \arrow[d] & E^* \arrow[r] \arrow[d] & \Psi \arrow[r] \arrow[d] & 0 \\
 & 0 & 0 & 0 &
\end{tikzcd}
batch 5 · p. 82 — lire la page12 / 12
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\begin{tikzcd}[column sep=huge]
0 \arrow[r] & \mathbb{Z} \arrow[r, "{\lambda=(d_i)}"] & \mathbb{Z}^r \arrow[r, "\alpha"] & E_{(s)} \arrow[r] \arrow[d, dashed, "u"] & 0 \\
 & \mathbb{Z} & \mathbb{Z}^r \arrow[l, "{\mu=(d_i\delta_i)=(d_i^t)}"'] & E^*_{(s)} \arrow[l, "\beta"'] & 0 \arrow[l]
\end{tikzcd}