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

Every constructible sheaf of $\mathbb{Q}-$modules over $\mathbb{R}$ is the direct sum of indecomposable sheaves, which are either sheaves with stalk $\mathbb{Q}$ at a point or constant sheaves with stalk $\mathbb{Q}$ on an open interval extended by lower ! or lower * at each endpoint. What happens if we remove the 'constructible' hypothesis? Is there a similar classification?

share|cite|improve this question
Are you looking for something that says, roughly, that the category of sheaves over $\mathbb R$ is a "limit" of the categories of constructible sheaves with respect to a given stratification? Here, the "limit" should be taken with respect to the poset of stratifications of $\mathbb R$. – André Henriques Mar 25 '11 at 14:12

Your Answer


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

Browse other questions tagged or ask your own question.