Fandom

Scratchpad

II.1.6

216,262pages on
this wiki
Add New Page
Discuss this page0 Share

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.

This problem has Hartshorne Height 2; II.1.2 can be used to solve it.

Sketch

  • a) Show exactness on stalks (this is II.1.2); show F_p/F'_p \cong (F/F')_p. This can be done by a universal property argument since you know what the universal property of $(F/F')_p$ is.
  • b) use a) to show 0\to \mbox{im}\alpha \to F \to F/\mbox{im}\alpha \to 0 is exact and use the 5-lemma with the original exact sequence to get the desired result.

Also on Fandom

Random wikia