I'd like to ask this question to make sure I understand a very basic thing about supports. Let $X$ be an algebraic space and F a quasi-coherent sheaf on it of finite type. In here …

Suppose I have a smooth projective variety $X$ and a semi-orthogonal decomposition of its bounded derived category of coherent sheaves $D^b(X)$. Then I can apply right or left mut …

For a complex manifold $M$, I'm trying to understand (from a differential geometry point of view) what its category of coherent sheaves is. If I understand correctly, then the shea …

I am trying to understand a particular case of this question. Let $T$ be an affine scheme of finite type over the ground field C. Let $X \to T$ be a morphism. I'll assume this to …

What is the best reference in English for the following theorem of Grauert–Riemenschneider: Theorem: Let $\phi:X \to Y$ be a proper bi-rational morphism of algebraic varieties o …

Let $X$ be a projective complex manifold. Is it true that any coherent sheaf $\mathcal{E}$ on $X$ whose Hilbert polynomial is a constant has a surjective morphsim $\mathcal{O}_X\ri …

suppose X is a smooth variety and F is a locally free sheaf on X. Let U be an open subset of X and i denote the inclusion map. Is i_*i^*F equal to F ? thanks.

Let $\mathcal{E}$ be a stable sheaf on a smooth complex projective threefold $X$ and $Ext^k_0(\mathcal{E},\mathcal{E})$ be the traceless Ext groups, defined by the kernel of the tr …

Are there any good tricks to construct a heart of a t-structure? (I'm thinking on the derived category of coherent sheaves of some variety) I'll start with the only one I know. If …

suppose $X$ is a smooth variety, with a finite open covering $U_i, i=1,....,k$. $F$ and $G$ are coherent sheaves on $X$, and $G$ is locally free. Suppose on each $U_i$, there is a …

Let $X$ be a connected projective scheme. Let $U$ be a finite type open substack of the algebraic stack of coherent sheaves on $X$ with a fixed Hilbert polynomial. Can one take $p> …

In his paper Gaussian maps and plethysm, Manivel uses the term "total exterior product" of line bundles, appearing for the first time on page 3. Given two (projective) varieties $V …

The question is in the title. I am trying to apply the Mitchell (Freyd-Mitchell?) embedding theorem, which states that for every small abelian category $A$, there exists a ring $ …

Let $\pi:X\to Y$ be a proper map of algebraic varieties (over $\mathbb C$) which is a bi-rational equivalence. are the following statements equivalent? The derived direct image …

Hello, Is there a proof that the push forward by a proper morphism of Noetherian schemes sends coherent sheaves to coherent ones, without passing in the argument through projectiv …