0
votes
0answers
70 views

On the intersection complex

Let $j:U\subset X$ an open immersion between $k$ schemes integral of finite type. Let $K\in D_{c}^{b}(X,\bar{\mathbb{Q}}_{l})$ a complex of $l$-adic sheaves, such that we have that $IC_{U}$ is a ...
4
votes
2answers
386 views

trying to understand the support of the sheaf of relative differentials

So I'm trying to understand a proof of Belyi's theorem from http://eprints.soton.ac.uk/29785/1/b45h1koe.pdf specifically lemma 3.4. The setup is as follows: Let $X/\mathbb{C}$ be a curve, and let $t ...
8
votes
1answer
721 views

Affine scheme on spec(A) of a ring A as the sheafification of a pre-sheave on spec(A)?

It is obvious that there is a parallel between the definition of structure sheaf of $\operatorname{Spec}(A)$ versus the sheafification of a pre-sheaf. The definition of the sheaf $\mathscr F^+$ ...
3
votes
2answers
709 views

morphisms of affine schemes question

So, in chapter 2, section 2 of Hartshorne, (prop 2.3), he describes how if $\varphi : A\rightarrow B$ is a homomorphism of rings, then you get a morphism of (affine schemes): ...