Cote n° 22 · pages 10–28 · 15 displayed formulas · [EGA IV]. [Chapitre] 0 IV. Cohen, différentielles, algèbres formellement simples (Compléments) : tirés à part (1963), tapuscrit annoté (s.d.), notes manuscrites (s.d.).
Inventory dating : 1963-[vers 1967]
Édition de démonstration

batch 1 · p. 10 — read it beside the facsimile1 / 15 · 6 distinct symbols, 10 written
\[M \otimes P \longrightarrow \prod_i M \otimes P_i\]
LaTeX source
\[
  M \otimes P \longrightarrow \prod_i M \otimes P_i
\]
batch 2 · p. 22 — read it beside the facsimile2 / 15 · 6 distinct symbols, 10 written
\[\Omega^{1}_{k} \otimes_{k} A \longrightarrow \Omega^{1}_{A}\]
LaTeX source
\[
  \Omega^{1}_{k} \otimes_{k} A \longrightarrow \Omega^{1}_{A}
\]
batch 2 · p. 22 — read it beside the facsimile3 / 15 · 9 distinct symbols, 11 written
\[D(x_i) = 1/\alpha\; x_i .\]
LaTeX source
\[
  D(x_i) = 1/\alpha\; x_i .
\]
batch 2 · p. 23 — read it beside the facsimile4 / 15 · 7 distinct symbols, 12 written
\[\Omega_{K/k} \otimes_{K} A \longrightarrow \Omega_{A/k}\]
LaTeX source
\[
  \Omega_{K/k} \otimes_{K} A \longrightarrow \Omega_{A/k}
\]
batch 2 · p. 23 — read it beside the facsimile5 / 15 · 8 distinct symbols, 10 written
\[D : A \longrightarrow \Omega_{K/k} \otimes_{K} A\]
LaTeX source
\[
  D : A \longrightarrow \Omega_{K/k} \otimes_{K} A
\]
batch 2 · p. 24 — read it beside the facsimile6 / 15 · 12 distinct symbols, 24 written
\[D\Big(\sum_{\lambda} a_{\lambda} t^{\lambda}\Big) \;=\; \sum_{\lambda} d_{K/k}(a_{\lambda})\, t^{\lambda} .\]
LaTeX source
\[
  D\Big(\sum_{\lambda} a_{\lambda} t^{\lambda}\Big)
  \;=\; \sum_{\lambda} d_{K/k}(a_{\lambda})\, t^{\lambda} .
\]
batch 2 · p. 24 — read it beside the facsimile7 / 15 · 7 distinct symbols, 9 written
\[f = \sum a_n t^{n} . \qquad \dots\]
LaTeX source
\[
  f = \sum a_n t^{n} . \qquad \dots
\]
batch 2 · p. 26 — read it beside the facsimile8 / 15 · 9 distinct symbols, 15 written
\[\Omega^{1}_{k/k \cap K^{p}} \otimes_{k} K \longrightarrow \Omega^{1}_{K}\]
LaTeX source
\[
  \Omega^{1}_{k/k \cap K^{p}} \otimes_{k} K \longrightarrow \Omega^{1}_{K}
\]
batch 2 · p. 26 — read it beside the facsimile9 / 15 · 8 distinct symbols, 23 written
\[\Omega^{1}_{k \cap K^{p}} \otimes_{k \cap K^{p}} K \to \Omega^{1}_{k} \otimes_{k} K \to \Omega^{1}_{K}\]
LaTeX source
\[
  \Omega^{1}_{k \cap K^{p}} \otimes_{k \cap K^{p}} K \to
  \Omega^{1}_{k} \otimes_{k} K \to \Omega^{1}_{K}
\]
batch 2 · p. 26 — read it beside the facsimile10 / 15 · 5 distinct symbols, 8 written
\[\Omega_{k} \otimes_{k} K \longrightarrow \Omega_{K}\]
LaTeX source
\[
  \Omega_{k} \otimes_{k} K \longrightarrow \Omega_{K}
\]
batch 2 · p. 26 — read it beside the facsimile11 / 15 · 13 distinct symbols, 46 written
\[\begin{cases} a_0 = y - \sum_{1}^{p-1} a_i x^{i} \\ a = x^{p} \end{cases} \qquad \text{d'où} \qquad y = \sum_{0}^{p-1} a_i x^{i}\]
LaTeX source
\[
  \begin{cases}
    a_0 = y - \sum_{1}^{p-1} a_i x^{i} \\
    a = x^{p}
  \end{cases}
  \qquad \text{d'où} \qquad y = \sum_{0}^{p-1} a_i x^{i}
\]
batch 2 · p. 26 — read it beside the facsimile12 / 15 · 16 distinct symbols, 52 written
\[K^{p} = \mathbf{F}(a, a_0, \dots, a_p) = \struck{\mathbf{F}(\alpha, x^{p}, y - \alpha x)}\; \mathbf{F}\Big(x^{p}, a_1, \dots, a_{p-1},\, y - \sum_{1}^{p-1} a_i x^{i}\Big)\]
LaTeX source
\[
  K^{p} = \mathbf{F}(a, a_0, \dots, a_p)
  = \struck{\mathbf{F}(\alpha, x^{p}, y - \alpha x)}\;
    \mathbf{F}\Big(x^{p}, a_1, \dots, a_{p-1},\, y - \sum_{1}^{p-1} a_i x^{i}\Big)
\]
batch 2 · p. 26 — read it beside the facsimile13 / 15 · 14 distinct symbols, 51 written
\[\struck{K = \mathbf{F}\big(\alpha^{1/p}, x, (y - \alpha x)^{1/p}\big)} \qquad \text{i.e.} \qquad K = \mathbf{F}\big(x, a_1^{1/p}, \dots, a_{p-1}^{1/p}, \ill{}\big)\]
LaTeX source
\[
  \struck{K = \mathbf{F}\big(\alpha^{1/p}, x, (y - \alpha x)^{1/p}\big)}
  \qquad \text{i.e.} \qquad
  K = \mathbf{F}\big(x, a_1^{1/p}, \dots, a_{p-1}^{1/p}, \ill{}\big)
\]
batch 2 · p. 28 — read it beside the facsimile14 / 15 · 11 distinct symbols, 37 written
\[\begin{cases} (x,y) \;\text{p-libre sur}\; \ill{} \\ \ill{}\; \lambda \notin \mathbf{F}(x,y) \end{cases}\]
LaTeX source
\[
  \begin{cases}
    (x,y) \;\text{p-libre sur}\; \ill{} \\
    \ill{}\; \lambda \notin \mathbf{F}(x,y)
  \end{cases}
\]
batch 2 · p. 28 — read it beside the facsimile15 / 15 · 10 distinct symbols, 13 written
\[\lambda = \mathbf{F}(a_1, \dots, a_{p-1})\]
LaTeX source
\[
  \lambda = \mathbf{F}(a_1, \dots, a_{p-1})
\]