All Questions

Assume that $X$ is a complex manifold. Let $\delta: X\to X\times X$ be the diagonal map. Assume that $\mathcal{A}_X$ is a $\mathbb C_X$-algebra and $\mathcal{M}_X$ is a left $\mathcal{A}_X\otimes_{\...

For a complex of sheaves $\cal{F}^{\bullet}$ on a variety $X$, a useful fact is that the stalks of the cohomology sheaves of $\mathcal{F}^{\bullet}$ agree with the cohomology groups of the complex of ...

I am in the following situation, I have two schemes $X$, $Y$ and two closed immersions $Z \rightarrow Y$, $Z \rightarrow X$. Everything is smooth. I am interested in calculating morphisms in the ...

In principle one uses the notion of derived category, and the other doesn't. Suppose $F: \mathcal A \to \mathcal B$ is a left exact (additive) functor between abelian categories, and suppose the ...

In "Residues and Duality" by Hartshorne, the derived tensor $\otimes$ only defined for the bounded above categories (see Chapter II, section 4, p.93), that is one has $$\otimes: D^{-}(X) \...

In the theory of cohomology of groups there are several important maps between cohomologies: restriction, inflation, transfer and Evens norm. The first three of them can be clearly seen on the level ...