\[
A^{p} \to A^{q} \to M \to 0
\]

\[
\underline{O}^{p} \to \underline{O}^{q} \to \widetilde{M} \to 0
\]

\[
\struck{\Gamma(M)} \quad M \xrightarrow{\sim} \Gamma(\widetilde{M})
\]

\[
\struck{\widetilde{M} = 0 \Rightarrow \Gamma(\widetilde{M}) = 0 \text{ i.e. } M = 0}
\]

\[
\underline{O}_{X}^{p} \xrightarrow{u} \underline{O}_{X}^{q} \to F \to 0
\]

\[
A^{p} \xrightarrow{u} A^{q}
\]

\[
F \simeq \widetilde{M}.
\]

\[
M \mapsto \widetilde{M} = M \otimes_{A_{X}} \underline{O}_{X}
\]

\[
M \mapsto M \otimes_{B_{X}} \mathcal{B}
\]

\[
\mathrm{Ass}\, F = \bigcup_{i} \mathrm{Ass}\, F_{i}
\]

\[
J = \varinjlim_{m} J_{m}
\]

\[
\mathcal{B}^{p} \xrightarrow{u} \mathcal{B}^{q} \to \mathcal{M} \to 0
\qquad (u = (u_{ij}),\ (i, j) \in P \times Q)
\]

\[
\mathcal{B}_{m}^{p} \to \mathcal{B}_{N+m}^{q} \to \mathcal{M}_{m} \to 0
\]

\[
\Gamma\mathcal{B}_{m}^{p} \to \Gamma\mathcal{B}_{m+N}^{q} \to \Gamma\mathcal{M}_{m} \to 0
\]

\[
\Gamma\mathcal{B}^{p} \to \Gamma\mathcal{B}^{q} \to \Gamma\mathcal{M} \to 0
\]

\[
(1) \qquad \dim(Y) + \mathrm{codim}_{X}(Y) \leq \dim(X).
\]

\[
(2) \qquad \mathrm{codim}_{T}(Y) \geq \mathrm{codim}_{Z}(Y) +
\mathrm{codim}_{T}(Z).
\]

\[
(4) \qquad \dim(Z) = \dim(Y) + \mathrm{codim}_{Z}(Y).
\]

\[
(5) \qquad \mathrm{codim}_{X}(Y) = \mathrm{codim}_{Z}(Y) +
\mathrm{codim}_{X}(Z).
\]

\[
(6) \qquad \dim(Y) + \mathrm{codim}_{X}(Y) = \dim(X) \text{ »,}
\]

\[
e_{1}, \quad ie_{1}, \quad e_{2}, \quad e_{1} + ike_{2}
\]

\[
\alpha + \delta, \quad \beta, \quad \gamma, \quad k\delta, \qquad (\gamma
\text{ ou } \delta \neq 0 ;\ \alpha\beta\gamma\delta \in \mathbb{Z})
\]

\[
c'(\alpha + \delta) - c''\beta, \quad c''(\alpha + \delta) + c'\beta, \quad
c'\gamma - k\delta c'', \quad c''\gamma + c'k\delta
\]

\[
\alpha c' - \beta c'', \quad \beta c' + \alpha c'', \quad c'\gamma, \quad
c''\gamma
\]