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

R

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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