MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X$ be a finite CW complex. Is there an integer $N,$ such that $H^i(X,F)=0$ for all $i>N$ and all abelian sheaves $F$ on $X?$ The cohomology is defined to be the derived functor of the global section.

share|cite|improve this question
up vote 3 down vote accepted

You can take $N=\dim X$, according to Proposition 3.1.5 in Dimca, [Alexandru. Sheaves in topology. Universitext. Springer-Verlag, Berlin, 2004. xvi+236 pp. MR2050072]

share|cite|improve this answer
Great! Thank you. – shenghao Mar 25 '10 at 5:10

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.