subsheaf of abelian groups
Suppose a sheaf of abelian groups is defined as a disjoint union of stalks over points , and is topologized in the appropriate manner. In particular, each stalk is an abelian group and the group operations are continuous. Then a subsheaf is an open subset of such that is a subgroup of .
Suppose is a complex manifold. Let be the sheaf of germs of meromorphic functions which are not identically zero. That is, for the stalk is the abelian group of germs of meromorphic functions at with the group operation being multiplication. Then , the sheaf of germs of holomorphic functions which are not identically 0 is a subsheaf of .
- 1 Glen E. Bredon. , Springer, 1997.
- 2 Robin Hartshorne. , Springer, 1977.
- 3 Lars Hörmander. , North-Holland Publishing Company, New York, New York, 1973.
|Title||subsheaf of abelian groups|
|Date of creation||2013-03-22 17:39:21|
|Last modified on||2013-03-22 17:39:21|
|Last modified by||jirka (4157)|