Cote n° 161-5 · pages 16–28 · 21 displayed formulas · Barsotti-Tate : tirés à part annotés (1967-1969), notes manuscrites (s.d.).
Inventory dating : 1967-1969
Édition de démonstration

batch 1 · p. 16 — read it beside the facsimile1 / 21 · 15 distinct symbols, 31 written
\[v(g) \geqslant n \iff (g-1)(T) \subset p^n T, \qquad w(g) \geqslant n \iff g \in I^n\]
LaTeX source
\[
v(g) \geqslant n \iff (g-1)(T) \subset p^n T, \qquad
w(g) \geqslant n \iff g \in I^n
\]
batch 2 · p. 22 — read it beside the facsimile2 / 21 · 14 distinct symbols, 41 written
\[\begin{array}{ccccccc} L & \subset & K & \subset & \bar{K} & \subset & \Omega \\ \cup & & \cup & & \cup & & \cup \\ W & \subset & V & \subset & \bar{V} & \subset & \hat{\bar{V}} \end{array}\]
LaTeX source
\[
\begin{array}{ccccccc}
L & \subset & K & \subset & \bar{K} & \subset & \Omega \\
\cup & & \cup & & \cup & & \cup \\
W & \subset & V & \subset & \bar{V} & \subset & \hat{\bar{V}}
\end{array}
\]
batch 2 · p. 22 — read it beside the facsimile3 / 21 · 10 distinct symbols, 26 written
\[\pi = \mathrm{Gal}(\bar{K}/K), \quad \pi' = \mathrm{Gal}(\bar{K}/L) \;\ldots\]
LaTeX source
\[
\pi = \mathrm{Gal}(\bar{K}/K), \quad \pi' = \mathrm{Gal}(\bar{K}/L) \;\ldots
\]
batch 2 · p. 22 — read it beside the facsimile4 / 21 · 8 distinct symbols, 12 written
\[\widetilde{\mathrm{BT}}_V \hookrightarrow \mathcal{M}^{(1)}_K\]
LaTeX source
\[
\widetilde{\mathrm{BT}}_V \hookrightarrow \mathcal{M}^{(1)}_K
\]
batch 2 · p. 22 — read it beside the facsimile5 / 21 · 8 distinct symbols, 9 written
\[\pi \xrightarrow{\ \rho\ } G(\mathbb{Q}_p)\]
LaTeX source
\[
\pi \xrightarrow{\ \rho\ } G(\mathbb{Q}_p)
\]
batch 2 · p. 22 — read it beside the facsimile6 / 21 · 12 distinct symbols, 43 written
\[G_M = \mathrm{Im}\bigl(G \to \underline{\mathrm{Aut}}_{\mathbb{Q}_p}(T_p(M))\bigr) \subset \underline{\mathrm{Aut}}_{\mathbb{Q}_p}(T_p(M))\]
LaTeX source
\[
G_M = \mathrm{Im}\bigl(G \to \underline{\mathrm{Aut}}_{\mathbb{Q}_p}(T_p(M))\bigr)
\subset \underline{\mathrm{Aut}}_{\mathbb{Q}_p}(T_p(M))
\]
batch 2 · p. 22 — read it beside the facsimile7 / 21 · 10 distinct symbols, 18 written
\[\bigl(\pi \xrightarrow{\ \rho_M\ } G_M(\mathbb{Q}_p) \quad \cdots\cdots \bigr)\]
LaTeX source
\[
\bigl(\pi \xrightarrow{\ \rho_M\ } G_M(\mathbb{Q}_p) \quad \cdots\cdots \bigr)
\]
batch 2 · p. 24 — read it beside the facsimile8 / 21 · 10 distinct symbols, 17 written
\[Q_\Omega = \mathcal{T} \wedge^{\mathbb{G}_{m,\Omega}} \mathfrak{P}^{!}_\Omega \qquad G_\Omega\]
LaTeX source
\[
Q_\Omega = \mathcal{T} \wedge^{\mathbb{G}_{m,\Omega}} \mathfrak{P}^{!}_\Omega
\qquad G_\Omega
\]
batch 2 · p. 24 — read it beside the facsimile9 / 21 · 9 distinct symbols, 21 written
\[U''_L \subset G''_L \;\text{—}\; Q_L \;\text{—}\; G_L, \qquad j_L : \mathbb{G}_{m,L} \to G''_L\]
LaTeX source
\[
U''_L \subset G''_L \;\text{—}\; Q_L \;\text{—}\; G_L, \qquad
j_L : \mathbb{G}_{m,L} \to G''_L
\]
batch 2 · p. 24 — read it beside the facsimile10 / 21 · 9 distinct symbols, 22 written
\[(u.\rho)(\gamma) = \tau(u)\,\rho(\gamma)\,\tau(u)^{-1}\]
LaTeX source
\[
(u.\rho)(\gamma) = \tau(u)\,\rho(\gamma)\,\tau(u)^{-1}
\]
batch 2 · p. 24 — read it beside the facsimile11 / 21 · 11 distinct symbols, 21 written
\[\boxed{\rho : \Delta \to \text{Op.\ de } \Gamma \text{ sur } (\Omega, Q_L, G_L)}\]
LaTeX source
\[
\boxed{\rho : \Delta \to \text{Op.\ de } \Gamma \text{ sur } (\Omega, Q_L, G_L)}
\]
batch 2 · p. 25 — read it beside the facsimile12 / 21 · 18 distinct symbols, 38 written
\[\mathbb{G}_{m,\Omega} \xrightarrow{\ j_\Omega\ } G''_\Omega \qquad M \mapsto \sum \mathrm{gr}^{i}_{j}(M_\Omega) \otimes S_\Omega(-i) = \mathrm{Hdg}(M)_\Omega\]
LaTeX source
\[
\mathbb{G}_{m,\Omega} \xrightarrow{\ j_\Omega\ } G''_\Omega
\qquad
M \mapsto \sum \mathrm{gr}^{i}_{j}(M_\Omega) \otimes S_\Omega(-i)
= \mathrm{Hdg}(M)_\Omega
\]
batch 2 · p. 25 — read it beside the facsimile13 / 21 · 13 distinct symbols, 22 written
\[\rho : \pi \to G(\mathbb{Q}_p) \subset H^{0}(\Omega, G_\Omega) = G(\Omega).\]
LaTeX source
\[
\rho : \pi \to G(\mathbb{Q}_p) \subset H^{0}(\Omega, G_\Omega) = G(\Omega).
\]
batch 2 · p. 26 — read it beside the facsimile14 / 21 · 13 distinct symbols, 28 written
\[\mathrm{DR}_L(M) = \bigl(R_L \wedge^{U''_L} Q_L\bigr) \wedge^{G_L} T_p(M)_L\]
LaTeX source
\[
\mathrm{DR}_L(M) = \bigl(R_L \wedge^{U''_L} Q_L\bigr) \wedge^{G_L} T_p(M)_L
\]
batch 2 · p. 26 — read it beside the facsimile15 / 21 · 7 distinct symbols, 10 written
\[R_L \wedge^{U'_L} Q_L = P_L\]
LaTeX source
\[
R_L \wedge^{U'_L} Q_L = P_L
\]
batch 2 · p. 26 — read it beside the facsimile16 / 21 · 3 distinct symbols, 7 written
\[G''\qquad P_K \qquad G_K\]
LaTeX source
\[
G''\qquad P_K \qquad G_K
\]
batch 2 · p. 26 — read it beside the facsimile17 / 21 · 6 distinct symbols, 8 written
\[P_K \simeq P^{(\sharp)}_K\]
LaTeX source
\[
P_K \simeq P^{(\sharp)}_K
\]
batch 2 · p. 26 — read it beside the facsimile18 / 21 · 8 distinct symbols, 16 written
\[P_\Omega = R_L \wedge^{U''_\Omega} Q_\Omega = R_L \wedge^{U''_\Omega}\]
LaTeX source
\[
P_\Omega = R_L \wedge^{U''_\Omega} Q_\Omega = R_L \wedge^{U''_\Omega}
\]
batch 2 · p. 27 — read it beside the facsimile19 / 21 · 8 distinct symbols, 19 written
\[1 \to G'_S(S) \to \mathcal{E} \to \Gamma \to 1 . \qquad (\mathcal{E})\]
LaTeX source
\[
1 \to G'_S(S) \to \mathcal{E} \to \Gamma \to 1 . \qquad (\mathcal{E})
\]
batch 2 · p. 28 — read it beside the facsimile20 / 21 · 10 distinct symbols, 33 written
\[\begin{cases} \varphi(\gamma\gamma') = \varphi(\gamma)\; {}^{\gamma}\varphi(\gamma') \\ \varphi(\pi) = \{e\} \end{cases}\]
LaTeX source
\[
\begin{cases}
\varphi(\gamma\gamma') = \varphi(\gamma)\; {}^{\gamma}\varphi(\gamma') \\
\varphi(\pi) = \{e\}
\end{cases}
\]
batch 2 · p. 28 — read it beside the facsimile21 / 21 · 9 distinct symbols, 21 written
\[H^{1}(\Gamma, G'_S(S)) \to H^{1}(\pi, G'_S(S))\]
LaTeX source
\[
H^{1}(\Gamma, G'_S(S)) \to H^{1}(\pi, G'_S(S))
\]