Index of notations

Listed in source order of EGA II. Section numbers refer to the defining occurrence. Symbols whose exact OCR form was unrecoverable are reconstructed from the translated sections.

• $\mathcal{A}(X),\mathcal{A}(\mathcal{F}),\mathcal{A}(\mathcal{B})$ ($X$ an $S$-prescheme, $\mathcal{F}$ an ${\mathcal{O}}_X$-module, $\mathcal{B}$ an ${\mathcal{O}}_X$-algebra): 1.1.1.
• $\mathcal{A}(h)$ ($h$ an $S$-morphism): 1.1.2.
• $\mathrm{Spec}(\mathcal{B})$ ($\mathcal{B}$ an ${\mathcal{O}}_S$-algebra): 1.3.1.
• $\tilde{\mathcal{M}}$ ($\mathcal{M}$ a $\mathcal{B}$-module, $\mathcal{B}$ an ${\mathcal{O}}_S$-algebra): 1.4.3.
• $\mathbb{T}(E),\mathbb{S}(E),{\mathbb{S}}_n(E)$ ($E$ an $A$-module): 1.7.1.
• $\mathbb{S}(\mathcal{E}),{\mathbb{S}}_n(\mathcal{E})$ ($\mathcal{E}$ an $\mathcal{A}$-module): 1.7.4.
• $\mathbb{V}(\mathcal{E})$ ($\mathcal{E}$ a quasi-coherent ${\mathcal{O}}_S$-module): 1.7.8.
• $S_n,S_{\bullet },M_n,S^{(d)},M^{(d)},M^{(d,k)}$ ($S$ a graded ring, $M$ a graded $S$-module): 2.1.1.
• $M(n),S(n)$ ($S$ a graded ring, $M$ a graded $S$-module): 2.1.1.
• ${\mathrm{Hom}}_S(M,N)$ ($S$ a graded ring, $M$, $N$ graded $S$-modules): 2.1.2.
• ${\mathfrak{N}}_{\bullet },{\mathfrak{r}}_{\bullet }(\mathfrak{j})$ ($\mathfrak{j}$ an ideal of $S_{\bullet }$): 2.1.10.
• $S_{(f)},M_{(f)}$ ($f$ a homogeneous element of $S_{\bullet }$): 2.2.1.
• $S_{(T)},M_{(T)},S_{(\mathfrak{p})},M_{(\mathfrak{p})}$ ($T$ a multiplicative subset of $S_{\bullet }$ consisting of homogeneous elements, $\mathfrak{p}$ a graded prime ideal of $S_{\bullet }$): 2.2.7.
• $\mathrm{Proj}(S)$ ($S$ a graded ring): 2.3.1.
• $V_{+}(E)$ ($E$ a subset of $S_{\bullet }$): 2.3.2.
• $D_{+}(f)$ ($f$ an element of $S$): 2.3.3.
• ${\mathfrak{j}}_{+}(Y)$ ($Y$ a subset of $\mathrm{Proj}(S)$): 2.3.10.
• $\tilde{M}$ ($M$ a graded $S$-module): 2.5.2.
• ũ ($u$ a homomorphism of degree 0): 2.5.4.
• ${\mathcal{O}}_X(n),\mathcal{O}(n)$ ($X=\mathrm{Proj}(S)$, $n$ an integer): 2.5.10.
• $\lambda$ (canonical homomorphism): 2.5.11.
• $\mu$ (canonical homomorphism): 2.5.12.
• $X_f$ ($X=\mathrm{Proj}(S)$, $f$ a homogeneous element of $S_d$, $d>0$): 2.5.16.
• ${\Gamma }_{\ast }(\mathcal{F})$ ($\mathcal{F}$ an ${\mathcal{O}}_X$-module, $X=\mathrm{Proj}(S)$): 2.6.1.
• ${\alpha }_n,\alpha ,{\alpha }^{♯}$ (canonical homomorphisms): 2.6.2.
• $\beta ,{\beta }^{♯}$ (canonical homomorphisms): 2.6.4.
• $G(\varphi ),a_{\varphi }$ (by abuse of notation) ($\varphi$ a homomorphism of graded rings): 2.8.1.
• $\mathrm{Proj}(\varphi )$ ($\varphi$ a homomorphism of graded rings): 2.8.2.
• $\mathcal{S}(n),{\mathcal{S}}^{(d)},{\mathcal{M}}^{(d)},\mathcal{M}(n)$ ($\mathcal{S}$ a graded ${\mathcal{O}}_Y$-algebra, $\mathcal{M}$ a graded $\mathcal{S}$-module): 3.1.1.
• $\mathrm{Proj}(\mathcal{S})$ ($\mathcal{S}$ a quasi-coherent graded ${\mathcal{O}}_Y$-algebra): 3.1.3.
• $X_f$ ($X=\mathrm{Proj}(\mathcal{S})$, $f$ a section of $\mathcal{S}$ over $Y$): 3.1.4.
• $\tilde{\mathcal{M}}$ ($\mathcal{M}$ a graded $\mathcal{S}$-module): 3.2.2.
• ${\mathcal{O}}_X(n),\mathcal{F}(n)$ ($X=\mathrm{Proj}(\mathcal{S})$, $\mathcal{F}$ an ${\mathcal{O}}_X$-module): 3.2.5.
• $\lambda ,\mu$ (canonical homomorphisms): 3.2.6.

• ${\Gamma }_{\ast }(\mathcal{F})$ ($\mathcal{F}$ an ${\mathcal{O}}_X$-module, $X=\mathrm{Proj}(\mathcal{S})$): 3.3.1.
• ${\alpha }_n,\alpha ,{\alpha }^{♯}$ (canonical homomorphisms): 3.3.2.
• $\beta ,{\beta }^{♯}$ (canonical homomorphisms): 3.3.4.
• $G(\varphi ),\mathrm{Proj}(\varphi )$ ($\varphi$ a homomorphism of graded ${\mathcal{O}}_Y$-algebras): 3.5.1.
• $\mathrm{Proj}(u)$ ($u$ a $q$-morphism from a graded ${\mathcal{O}}_Y$-algebra to a graded ${\mathcal{O}}_{Y^{\prime }}$-algebra): 3.5.6.
• $r_{\mathcal{L}}$ ($\mathcal{L}$ an invertible $\mathcal{O}$-module): 3.7.1.
• $\mathbb{P}(\mathcal{E}),\mathbb{P}(E),{\mathbb{P}}_S^n,{\mathbb{P}}^n$: 4.1.1.
• $\mathbb{P}(u)$ ($u$ a surjective homomorphism of ${\mathcal{O}}_Y$-modules): 4.1.2.
• $Sy{m}_n(\mathcal{E}),\Gamma (X,\mathcal{S}{\otimes }^n)$ ($\mathcal{E}$ a quasi-coherent ${\mathcal{O}}_Y$-module): 4.2.5.
• $\varsigma$ (Segre morphism): 4.3.1.
• $\mathcal{F}(n)$ ($\mathcal{F}$ an ${\mathcal{O}}_X$-module, $X$ equipped with an invertible ${\mathcal{O}}_X$-module): 4.5.1.
• $e$ (identity automorphism): 4.5.1.
• $P_c(u,T),{\sigma }_i(u)$ ($u$ an endomorphism of a free module of finite basis): 6.4.1.
• $P_c(u,T),{\sigma }_i(u),det(u)$ ($u$ an endomorphism of a finite-type module over an integral ring or a reduced Noetherian ring): 6.4.2, 6.4.7.
• ${\sigma }_i(u),det(u)$ ($u$ an endomorphism of a locally free $\mathcal{A}$-module): 6.4.8.
• ${\sigma }_i,det$ (sheaf homomorphisms): 6.4.8, 6.4.9, 6.4.10.
• ${\sigma }_i(u),det(u)$ ($u$ an endomorphism of a finite-type ${\mathcal{O}}_X$-module over a locally integral prescheme, or a locally Noetherian and reduced prescheme): 6.4.9, 6.4.10.
• $N_{{\mathcal{A}}^{\prime }/\mathcal{A}}(f)$ ($f$ a section of the $\mathcal{A}$-algebra ${\mathcal{A}}^{\prime }$): 6.5.1.
• $N_{{\mathcal{A}}^{\prime }/\mathcal{A}}({\mathcal{L}}^{\prime })$ (${\mathcal{L}}^{\prime }$ an invertible ${\mathcal{A}}^{\prime }$-module): 6.5.2.
• $N_{{\mathcal{A}}^{\prime }/\mathcal{A}}(h^{\prime })$ ($h^{\prime }$ a homomorphism of invertible ${\mathcal{A}}^{\prime }$-modules): 6.5.3.
• $N_{X^{\prime }/X}({\mathcal{L}}^{\prime })$ ($X^{\prime }$ finite over $X$, ${\mathcal{L}}^{\prime }$ an invertible ${\mathcal{O}}_{X^{\prime }}$-module): 6.5.5.
• $N_{X^{\prime }/X}(h^{\prime })$ ($h^{\prime }$ a homomorphism of invertible ${\mathcal{O}}_{X^{\prime }}$-modules): 6.5.5.
• ${\mathcal{S}}_n$ ($X=\mathrm{Proj}(\mathcal{S})$, $\mathcal{S}$ the direct sum of a graded family of ideals ${\mathcal{I}}_n\subset {\mathcal{O}}_Y$): 8.1.5.
• $S^{\ge },S^{\le },S_{[n]},S_{[f]},M^{\ge },M^{\le },M_{[n]},M_{[f]}$ ($S$ a graded ring, $M$ a graded $S$-module, $f$ a homogeneous element of $S_{\bullet }$): 8.2.1.
• $S^{♮}$ ($S$ a graded ring): 8.2.2.
• $M^{♮}$ ($M$ a graded $S$-module): 8.2.4.
• $S_{[f]},S_{[f]}^{♮},f^{♮}$ ($S$ a graded ring, $f$ homogeneous in $S$): 8.2.6.
• $M_n^{♮},M_{[n]}^{♮}$ ($M$ a graded $S$-module): 8.2.8.
• $\mathcal{C}(\mathcal{S})$ ($\mathcal{S}$ a graded ${\mathcal{O}}_Y$-algebra): 8.3.1.
• ${\mathbb{G}}_m$ (group scheme): 8.3.9.
• ${\mathbb{V}}_X(\mathcal{S})$ ($X=\mathrm{Proj}(\mathcal{S})$, $\mathcal{S}$ a graded ${\mathcal{O}}_X$-algebra): 8.6.1.
• ${\mathbb{V}}_X,C_X,C_X^{\ast },E_X,E_X^{\ast }$ ($X=\mathrm{Proj}(\mathcal{S})$, $\mathcal{S}$ a graded ${\mathcal{O}}_X$-algebra with ${\mathcal{S}}_0={\mathcal{O}}_X$): 8.6.1.
• ${\mathbb{V}}_Y(\mathcal{S})$ ($\mathcal{S}$ a graded ${\mathcal{O}}_Y$-algebra): 8.7.2.
• $\mathcal{P}{roj}_0(\mathcal{M}),\mathcal{P}roj(\mathcal{M}),\tilde{\mathcal{M}},\tilde{\mathcal{M}}\square$ ($\mathcal{M}$ a graded $\mathcal{S}$-module): 8.12.1.
• ${\mathcal{M}}_{\square }$ ($X=\mathrm{Proj}(\mathcal{S})$, $\mathcal{M}$ a graded $\mathcal{S}$-module): 8.12.5.
• ${\mathcal{H}}_{\mathcal{M},\mathcal{N}}$ ($\mathcal{M}$, $\mathcal{N}$ graded $\mathcal{S}$-modules): 8.12.9.
• $(\mathcal{N}{)}^{♭}$ ($\mathcal{N}$ a sub-$\mathcal{S}$-module of a graded $\mathcal{S}$-module): 8.13.1.
• $(\mathcal{N}{)}^h$ ($\mathcal{N}$ a sub-$\mathcal{S}$-module of a graded $\mathcal{S}$-module; homogenization): 8.13.2.
• ${\Gamma }_{\ast }(\mathcal{F})$ ($X=\mathrm{Proj}(\mathcal{S})$, $\mathcal{F}$ an ${\mathcal{O}}_X$-module): 8.14.5.
• ${\mathcal{M}}_{X^{\prime }},{\Gamma }_{\ast }^{\prime }(\mathcal{F}),\mathcal{P}{roj}^{\prime }(\mathcal{M}),{\alpha }^{\prime },{\beta }^{\prime }$ ($X^{\prime }\subset X=\mathrm{Proj}(\mathcal{S})$ open, $\mathcal{M}$ a graded $\mathcal{S}$-module, $\mathcal{F}$ an ${\mathcal{O}}_{X^{\prime }}$-module): 8.14.6.