Index of notations

Listed in source order of EGA III. Section numbers refer to the defining occurrence. The two parts of the volume share a single index here; each entry is tagged with its home chapter prefix.

Chapter 0 (continued)

• Set (EGA’s Ens): 0_III.8.1.1.
• $h_X(Y)$, $h_X(u)$ ($X$, $Y$ objects of a category $\mathcal{C}$, $u$ a morphism of $\mathcal{C}$): 0_III.8.1.1.
• $h^{\bullet }(u)$ ($u$, $w$ morphisms of $\mathcal{C}$): 0_III.8.1.2.
• $Z_k(E_r^{p,q})$, $B_k(E_r^{p,q})$ ($k\ge r$): 0_III.11.1.1.
• $Z_{\infty }(E_r^{p,q})$, $B_{\infty }(E_r^{p,q})$: 0_III.11.1.1.
• $K^{\bullet }$, $K_{\bullet }$ (complexes): 0_III.11.2.1.
• $K^{\bullet ,\bullet }$, $K_{\bullet ,\bullet }$ (bicomplexes): 0_III.11.2.1.
• $B^p(K^{\bullet })$, $Z^p(K^{\bullet })$, $H^p(K^{\bullet })$, $H^{\bullet }(K^{\bullet })$: 0_III.11.2.1.
• $B_p(K_{\bullet })$, $Z_p(K_{\bullet })$, $H_p(K_{\bullet })$, $H_{\bullet }(K_{\bullet })$: 0_III.11.2.1.
• $T(K^{\bullet })$, $T(K_{\bullet })$ ($T$ a functor): 0_III.11.2.1.
• $E(K^{\bullet })$ ($K^{\bullet }$ a filtered complex): 0_III.11.2.2.
• $K^{p,q}$, $K_{p,q}$, $Z_I^p(K^{\bullet ,\bullet })$, $B_I^p(K^{\bullet ,\bullet })$, $H_I^p(K^{\bullet ,\bullet })$, $Z_{II}^q(K^{\bullet ,\bullet })$, $B_{II}^q(K^{\bullet ,\bullet })$, $H_{II}^q(K^{\bullet ,\bullet })$: 0_III.11.3.1.
• $H_I^p(K^{\bullet })$, $Z_{II}^q(H_I^p(K^{\bullet }))$, $B_{II}^q(H_I^p(K^{\bullet }))$, $H_{II}^q(H_I^p(K^{\bullet }))$, $H^{\bullet }(K^{\bullet })$: 0_III.11.3.1.
• $F_I^p(K^{\bullet })$, $F_{II}^q(K^{\bullet })$, ${}^{\prime }E(K^{\bullet })$, ${}^{\prime \prime }E(K^{\bullet })$: 0_III.11.3.2.
• $K_{\bullet ,\bullet }$, $H_I^p(K_{\bullet ,\bullet })$, $H_{II}^q(K_{\bullet ,\bullet })$, $H_{I,II}^{p,q}(K_{\bullet ,\bullet })$, $H_n(K_{\bullet ,\bullet })$: 0_III.11.3.5.
• $R^{\bullet }T(K^{\bullet })$ ($T$ a covariant additive functor): 0_III.11.4.3.
• $R^{\bullet }T(K^{\bullet },K^{\prime \bullet })$ ($T$ a covariant additive bifunctor): 0_III.11.4.6.
• $L_{\bullet }T(K_{\bullet })$ ($T$ a covariant additive functor): 0_III.11.6.2.
• $L_{\bullet }T(K_{\bullet },K_{\bullet }^{\prime })$ ($T$ a covariant additive bifunctor): 0_III.11.6.6.
• $L_{\bullet }T(K_{\bullet ,\bullet })$ ($T$ a covariant additive functor): 0_III.11.7.2.
• $|\sigma |$, $\Sigma (A)$, $C_{\bullet }(A)$, $L_{\bullet }(A)$ ($A$ a finite set, $\sigma$ a simplex of $A$): 0_III.11.8.1.
• $C^{\bullet }(A,B;\mathcal{S})$, $L^{\bullet }(A,B;\mathcal{S})$ ($A$, $B$ finite sets, $\mathcal{S}$ a system of coefficients): 0_III.11.8.4.
• $P^{\bullet }(A,B;\mathcal{S})$ ($A$, $B$ finite sets, $\mathcal{S}$ a system of coefficients): 0_III.11.8.6.
• $C^{\bullet }(A,B;{\mathcal{S}}^{\bullet })$, $L^{\bullet }(A,B;{\mathcal{S}}^{\bullet })$ ($A$, $B$ finite sets, ${\mathcal{S}}^{\bullet }$ a complex of systems of coefficients): 0_III.11.8.8.
• $P^{\bullet }(A,B;{\mathcal{S}}^{\bullet })$ ($A$, $B$ finite sets, ${\mathcal{S}}^{\bullet }$ a complex of systems of coefficients): 0_III.11.8.10.
• $\chi (M^{\bullet })$ ($M^{\bullet }$ a finite complex of finite-length modules): 0_III.11.10.1.
• $C^{\bullet }(\mathfrak{U},\mathcal{F})$ ($\mathcal{F}$ a sheaf of abelian groups on $X$, $\mathfrak{U}$ an open cover of $X$): 0_III.12.1.2.
• $R^p{f}_{\ast }(\mathcal{F})$ ($f:X\to Y$ a morphism of ringed spaces, $\mathcal{F}$ a sheaf of ${\mathcal{O}}_X$-modules): 0_III.12.2.1.
• ${\mathcal{H}}^{\bullet }(f,{\mathcal{K}}^{\bullet })$, ${\mathcal{H}}^{\bullet }(f,\mathcal{F})$, ${}^{\prime }{\mathcal{H}}^{\bullet }(f,{\mathcal{K}}^{\bullet })$, ${}^{\prime \prime }{\mathcal{H}}^{\bullet }(f,{\mathcal{K}}^{\bullet })$ ($f:X\to Y$ a morphism of ringed spaces, ${\mathcal{K}}^{\bullet }$ a complex of ${\mathcal{O}}_X$-modules): 0_III.12.4.1.
• $H^{\bullet }(X,{\mathcal{K}}^{\bullet })$, $H^{\bullet }(V,{\mathcal{K}}^{\bullet })$ ($X$ a ringed space, ${\mathcal{K}}^{\bullet }$ a complex of ${\mathcal{O}}_X$-modules, $V$ an open subset of $X$): 0_III.12.4.2.
• $g{r}^{\bullet }(\mathbf{A})$ ($\mathbf{A}$ a projective system satisfying (ML)): 0_III.13.4.2.
• $E(\mathbf{A})$ ($\mathbf{A}$ a filtered object): 0_III.13.6.4.

Chapter III, Part 1

• $K_{\bullet }(\mathbf{f})$, $i_{\mathbf{f}}$ ($\mathbf{f}$ a finite family of elements of a ring): III.1.1.1.
• $K^{\bullet }(\mathbf{f},M)$, $K_{\bullet }(\mathbf{f},M)$ ($\mathbf{f}$ a finite family of elements of a ring $A$, $M$ an $A$-module): III.1.1.2.
• $H^{\bullet }(\mathbf{f},M)$, $H_{\bullet }(\mathbf{f},M)$ ($\mathbf{f}$ a finite family of elements of a ring $A$, $M$ an $A$-module): III.1.1.3.
• $C^{\bullet }((\mathbf{f}),M)$, $H^{\bullet }((\mathbf{f}),M)$ ($\mathbf{f}$ a finite family of elements of a ring $A$, $M$ an $A$-module): III.1.1.6.
• $H^{\bullet }(U,\mathcal{F}(\ast ))$, $H^{\bullet }(\mathfrak{U},\mathcal{F}(\ast ))$ ($\mathcal{F}$ a quasi-coherent ${\mathcal{O}}_X$-module, $U$ an open subset of $X$, $\mathfrak{U}$ an open cover of $X$): III.2.1.1.

Chapter III, Part 2

• $To{r}_{\bullet }^A(K_{\bullet },K_{\bullet }^{\prime })$: III.6.3.1.
• $\mathcal{T}o{r}_{\bullet }^{\mathcal{O}}({\mathcal{F}}_{\bullet },{\mathcal{G}}_{\bullet })$, $\mathcal{T}o{r}_{\bullet }^{\mathcal{O}}({\mathcal{F}}_{\bullet },{\mathcal{G}}_{\bullet })$: III.6.4.1 and III.6.5.1.
• $To{r}_{\bullet }^Y({\mathcal{F}}_{\bullet },{\mathcal{G}}_{\bullet })$: III.6.5.1.
• $Sp({\mathcal{F}}^{\bullet },{\mathcal{F}}^{\prime \bullet })$, $Sp({\mathcal{F}}_{\bullet },{\mathcal{F}}_{\bullet }^{\prime })$: III.6.5.15.
• $H^{\bullet }(u^{(1)},u^{(2)})$, $H^{\bullet }(K^{(1)\bullet },K^{(2)\bullet })$: III.6.6.1.
• $To{r}_{\bullet }^Y(u^{(1)},u^{(2)})$, $To{r}_{\bullet }^Y(u^{(1)},u^{(2)};{\mathcal{F}}^{(1)},{\mathcal{F}}^{(2)})$: III.6.6.2.
• $To{r}_{\bullet }^Y(u^{(1)},u^{(2)};{\mathcal{F}}^{(1)\bullet },{\mathcal{F}}^{(2)\bullet })$, $To{r}_{\bullet }^Y(u^{(1)},u^{(2)};{\mathcal{F}}_{\bullet }^{(1)},{\mathcal{F}}_{\bullet }^{(2)})$: III.6.6.2.
• $To{r}_{\bullet }^Y(f^{(1)},f^{(2)};{\mathcal{F}}^{(1)},{\mathcal{F}}^{(2)})$: III.6.6.8, III.6.7.1, and III.6.7.3.
• $To{r}_{\bullet }^Y((f_i);({\mathcal{F}}_i{)}_{i\in I})$, $To{r}_{\bullet }^Y(f_1,\cdots ,f_n;{\mathcal{F}}^{(1)},\cdots ,{\mathcal{F}}^{(n)})$: III.6.7.11.
• Ab, $A{b}_{\bullet }$: III.7.1.1.
• $T_{\varphi }$, $T_B^A$, $T(\bullet ){\otimes }_{A}B$ ($T$ a functor $A{b}_A\to Ab$): III.7.1.3.
• $T_{\varphi }^{\bullet }$: III.7.2.2.
• $T_{\varphi }^p$: III.7.1.4.
• ${\mathcal{H}}^{\bullet }(\mathcal{G},\mathcal{F})$, ${\mathcal{H}}^{\bullet }(\mathcal{G}|U,\mathcal{F}|U)$: III.7.7.2.
• $E^p(f,{\mathcal{F}}_{\bullet };y)$, $E^p(Y,{\mathcal{F}}_{\bullet };y)$, $E^p({\mathcal{F}}_{\bullet };y)$: III.7.9.5.
• $PH(f,{\mathcal{F}}_{\bullet };y)$, $PH({\mathcal{F}}_{\bullet };y)$: III.7.9.12.