All Questions

Suppose that $\pi:X\to S$ is a flat morphism between Noetherian, integral schemes (of characteristic zero, if need be). Let $\mathcal{E}$ be a locally free sheaf on $X$, and $$\nabla:\mathcal{E} \to \...

Let $\varphi:X\to Y$ be a morphism of schemes of relative dimension 1, and $\mathcal{L}' \xrightarrow{g} \mathcal{L}$ an injection of line bundles on $X$. The sequence $$0\to \mathcal{L}' \xrightarrow{...

I'm trying to understand following Example in Hartshorne (Chapter III, Example 9.8.2 & Example 12.9.2): Let $X_1 \subset \mathbb{P}^{3}$ be a twisted cubic curve not containing the point $(0:...:1)...

Let $X$ be a smooth scheme over $\mathbb{C}$ and a constructible sheaf $K$ of complex vector spaces on $X\times\mathbb{A}^1$ and a function $g:X\rightarrow \mathbb{A}^1$. Suppose that $K$ is locally ...

Let $X$ be an affine Noetherian scheme, $Y$ a separated Noetherian scheme, $f:X\rightarrow Y$ a morphism of schemes inducing a homeomorphism on the underlying topological spaces. Let $F$ be a ...

Let consider a quasicompact open $j:U\rightarrow\mathbb{A}^{\mathbb{N}}$ over a field $k$, Is there an example where $Rj_{*}\mathbb{Z}/n\mathbb{Z}$ is not constructible, where $n$ is prime to the ...