General Properties
- If f: A → B is a homomorphism between two sheaves of rings on the same space X, the kernel of f is an ideal sheaf in A.
- Conversely, for any ideal sheaf J in a sheaf of rings A, there is a natural structure of a sheaf of rings on the quotient sheaf A/J. Note that the canonical map
-
- Γ(U, A)/Γ(U, J) → Γ(U, A/J)
- for open subsets U is injective, but not surjective in general. (See sheaf cohomology.)
Read more about this topic: Ideal Sheaf
Famous quotes containing the words general and/or properties:
“As a general rule never take your whole fee in advance, nor any more than a small retainer. When fully paid beforehand, you are more than a common mortal if you can feel the same interest in the case, as if something was still in prospect for you, as well as for your client.”
—Abraham Lincoln (1809–1865)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)