Cote n° 23 · pages 18–80 · 27 diagrammes commutatifs · EGA IV. Compléments : notes manuscrites (s.d.), lettres (1966, 1968), tapuscrit (s.d.).
Datation de l’inventaire : 1966-1968
Édition de démonstration

batch 1 · p. 18 — lire la page1 / 27
LaTeX source
\begin{tikzcd}
  X \arrow[d, "f"'] & X_{0} \arrow[l] \arrow[d, "f_{0}"] \\
  S & T \arrow[l] & S = T_{0} \arrow[l]
\end{tikzcd}
batch 1 · p. 18 — lire la page2 / 27
LaTeX source
\begin{tikzcd}
  \underline{\mathcal{O}}_{X} \arrow[r] & \underline{\mathcal{O}}_{X_0} \\
  \underline{\mathcal{O}}_{S} \arrow[r] \arrow[u] &
  \underline{\Lambda} \arrow[r, "\varepsilon"] \arrow[u] &
  \underline{\mathcal{O}}_{S}
\end{tikzcd}
batch 2 · p. 23 — lire la page3 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  Y \arrow[d, "p"'] & \pi^{(n)}(Y/X/S) \arrow[d] \\
  S & X \arrow[l, "f"'] & \Delta^{(n)}_{X/S} \arrow[l, "\delta^{n}_{X/S}"']
\end{tikzcd}
batch 2 · p. 23 — lire la page4 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  & X \times_{S} Y \arrow[d] & \pi^{(n)}(Y/X/S) \arrow[l] \arrow[d]
    & Y \arrow[l, "\varepsilon^{n}(Y/X/S)"'] \arrow[d] \\
  X & X \times_{S} X \arrow[l, "pr_{1}"']
    & \Delta^{(n)}_{X/S} \arrow[l, "i^{(n)}_{X/S}"'] \arrow[d]
    & X \arrow[l, "\Delta_{X/S}"'] \arrow[d] \\
  X' & X' \times_{S} X \arrow[l] & (\Gamma_{\varphi})^{(n)} \arrow[l]
    & X' \arrow[l]
\end{tikzcd}
batch 2 · p. 23 — lire la page5 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  Y \arrow[r, "\varepsilon^{n}(Y/X/S)"] \arrow[d] & \pi^{n}(Y/X/S)
    \arrow[r, "d^{n}(Y/X/S)"] \arrow[d] & Y \arrow[d] \\
  X \arrow[r, "\Delta_{X/S}"] & \Delta^{(n)}_{X/S}
    \arrow[r, "\delta^{(n)}_{X/S}"] & X
\end{tikzcd}
batch 2 · p. 25 — lire la page6 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  P^{(n)}(Y/X/S) \arrow[r, "\varepsilon^{n}(Y/X/S)"] \arrow[dr] & Y \arrow[d] \\
  & X
\end{tikzcd}
batch 2 · p. 27 — lire la page7 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  Y^{\{\Delta^{(n)}_{X/S}\}} \arrow[dr, dashed] & & & \\
  P^{n}(Y/X/S) \arrow[r] \arrow[d, "p"'] & Y \arrow[d]
    & \pi^{(n)}(Y/X/S) \arrow[l] \arrow[d] & Y \arrow[l] \arrow[d] \\
  X & X \times_{S} X \arrow[l, "pr_{1}"']
    & \Delta^{(n)}_{X/S} \arrow[l] & X \arrow[l]
\end{tikzcd}
batch 2 · p. 27 — lire la page8 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  A \arrow[r] & A \otimes A \\
  B \arrow[u] & A' \arrow[u]
\end{tikzcd}
batch 2 · p. 27 — lire la page9 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  (B \otimes_{A} A') \otimes A \arrow[d] & A' \otimes A \arrow[l] \arrow[r]
    & A' & A' \otimes B \arrow[l] \\
  (B \otimes_{A} B) \otimes A & B \otimes A \arrow[l] \arrow[r] & B
    & B \otimes B \arrow[l]
\end{tikzcd}
batch 2 · p. 28 — lire la page10 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  & Y^{\Delta^{n}_{X/S}} \arrow[dr] & \\
  P^{n}(Y/X/S) \arrow[r] & Y \arrow[d] & \pi^{n}(Y/X/S) \arrow[l] \arrow[d] \\
  & X & \Delta^{n}_{X/S} \arrow[l]
\end{tikzcd}
batch 2 · p. 28 — lire la page11 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  P^{n}(Y/S) & P^{n}(X/S) \arrow[l] \\
  \mathcal{O}_{Y} \arrow[u] & \mathcal{O}_{X} \arrow[l] \arrow[u]
\end{tikzcd}
batch 2 · p. 28 — lire la page12 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  f^{*}P^{n}(Y/S) \arrow[d] & P^{n}(Y/S) \arrow[l, "?"']
    \arrow[d] & f^{*}P^{n}(X/S) \arrow[l, Rightarrow] \arrow[d] \\
  \underline{\mathcal{O}}_{X} & \underline{\mathcal{O}}_{X} \arrow[l]
    & \underline{\mathcal{O}}_{X} \arrow[l]
\end{tikzcd}
batch 2 · p. 29 — lire la page13 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  M \arrow[d] \\
  A \arrow[r] & B
\end{tikzcd}
batch 2 · p. 30 — lire la page14 / 27
LaTeX source
\begin{tikzcd}
  X_{S'} \arrow[r, "u"] \arrow[d, "f_{S'}"'] & X_{S'} \arrow[d, "f_{S'}"] \\
  Y_{S'} \arrow[r, "v"] & Y_{S'}
\end{tikzcd}
batch 2 · p. 31 — lire la page15 / 27
LaTeX source
\begin{tikzcd}
  X_{S'} \arrow[r, "h_{S'}"] \arrow[d, "u"'] & X'_{S'} \arrow[d, "u'"] \\
  X_{S'} \arrow[r, "h_{S'}"] & X'_{S'}
\end{tikzcd}
batch 2 · p. 32 — lire la page16 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  Y_{S'} \arrow[r] & Y_{S'}
\end{tikzcd}
batch 2 · p. 39 — lire la page17 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  X' & X'' \arrow[l] \\
  S' \arrow[u] & S'' \arrow[l] \arrow[u] \\
  S \arrow[r] & S' \arrow[r] & S''
\end{tikzcd}
batch 2 · p. 40 — lire la page18 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  E^{n} & E^{n}_{S^{d,n}} \arrow[l] & E^{n} \arrow[l] & S \arrow[l] \\
  S & S^{d,n} \arrow[l] & S \arrow[l] &
\end{tikzcd}
batch 3 · p. 48 — lire la page19 / 27
LaTeX source
\begin{tikzcd}
X \arrow[d, "u"'] \\
Y
\end{tikzcd}
batch 3 · p. 48 — lire la page20 / 27
LaTeX source
\begin{tikzcd}[column sep=small]
X \arrow[d, "\text{non ram.}"'] & & \\
Y & Y' \arrow[l, "\text{loc. noeth. fini épim.}"'] & Y'' \arrow[l, bend left=20] \arrow[l, bend right=20]
\end{tikzcd}
batch 4 · p. 75 — lire la page21 / 27
LaTeX source
\begin{tikzcd}
  \mathrm{OF}(S) \arrow[r, hook] \arrow[d] & \mathrm{OF}(T) \arrow[d] \\
  \mathrm{OF}(S') \arrow[r, hook] & \mathrm{OF}(T')
\end{tikzcd}
batch 4 · p. 76 — lire la page22 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  A_0 \quad B_0 \arrow[d] & & A \quad B \arrow[d, no head] & \\
  S_0 \arrow[r] \arrow[dd] & T_0' \arrow[ddl] & S \arrow[dd, no head] \arrow[r, leftrightarrow] & T' \arrow[ddl] \\
  & & & \\
  T_0 \arrow[rr, no head] & & \operatorname{Spec} k = T &
\end{tikzcd}
batch 4 · p. 76 — lire la page23 / 27
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
  S & T \arrow[l] \\
  S' \arrow[u] \arrow[r] & T' \arrow[u] \\
  S'' \arrow[u] \arrow[r] & T'' \arrow[u, no head]
\end{tikzcd}
batch 4 · p. 77 — lire la page24 / 27
LaTeX source
\begin{tikzcd}
  \bar Y \arrow[r] \arrow[d] & \bar X \arrow[d] \\
  Y \arrow[r] & X
\end{tikzcd}
batch 4 · p. 79 — lire la page25 / 27
LaTeX source
\begin{tikzcd}
  Y' \arrow[r, no head] \arrow[d, no head] & X' \arrow[d, no head] \\
  Y \arrow[r, no head] & X
\end{tikzcd}
batch 4 · p. 80 — lire la page26 / 27
LaTeX source
\begin{tikzcd}
  \bar Y \arrow[r] \arrow[d] & \bar X \arrow[d] \\
  Y \arrow[r] & X
\end{tikzcd}
batch 4 · p. 80 — lire la page27 / 27
LaTeX source
\begin{tikzcd}
  \bar Y \arrow[r, "u^{\prime}"'] \arrow[d, "p_Y"'] & \bar X \arrow[d, "p"] & \bar F \\
  Y \arrow[r, "u"'] & X &
\end{tikzcd}