Glossary of Notation
Unless otherwise stated all rings are commutative with 1. A multiplicatively
closed set of a ring R always contains 1R. A ring homomorphism R S maps 1R
to 1S . This is also called an algebra S/R. We try to use the standard notation and
language of algebraic geometry.
N {0, 1, 2, . . . }
N+ {1, 2, 3, . . . }
U(X) set of open subsets of X 1
Ab(X) category of abelian sheaves on X 1
sx germ of a section s at x 1
Supp(s) support of a section s 1
F (U) group of sections on an open set U 1
Fx stalk of F at x 1
ΓY (X, F ) group of sections with support in Y 1
HY i (X, F ) i-th cohomology with support in Y 1
Hx(X, i F ) i-th local cohomology at a point x 1
M sheaf associated to a module M 1
F flasque sheaf associated to F 2
j!F extension of a sheaf by zero 2
F|U restriction of a sheaf to an open set U 2
Mod(X) category of sheaves of modules on a ringed space X 4
Hi(X, F ) i-th global cohomology 4
j∗F direct image sheaf 5
M an S-module considered as an R-module via R S 6
Spec R spectrum of a ring R 6
D(f) non-vanishing set of f on an affine scheme 7
Mf localization of a module at f 7
Ann annihilator of an element or ideal or module 7
V (a) vanishing set of an ideal a on an affine scheme 8
V (f) vanishing set of a set f of polynomials 8
Γa(M) sections of a module with support in V (a) 8
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