All Questions

Let $\pi:X\rightarrow S$ be a smooth scheme over $S$ and let's assume for simplicity that $S=\mathrm{Spec} R$ is affine, Noetherian and regular. Let $\mathcal F$ be a coherent sheaf on $X$ and let's ...

Is there any text that gives some applications of sheaves theory in commutative ring theory? In the other word, is any results in commutative ring theory that be verified by sheaves method?

I am reading local cohomology and am confused on a silly point. Let $U$ be an affine, non-singular variety and $Z \subset U$ a hypersurface section on $U$ (i.e., complete intersection in $U$ of ...

We have the famous classification of rings satisfying $a^2=a$ (for each element $a$) in terms of Stone spaces, via $X \mapsto C(X,\mathbb{F}_2)$. Similarly, rings satisfying $a^3=a$ are classified by ...

I have been trying to understand the proof of the following theorem for the last month, I read some basics of sheaves theory and their cohomology, but still can't get the idea of this important ...