All Questions

There are several approaches of increasing sophistication and simplicity to defining derived functors. I know of universal $\delta$-functors and Kan extensions along localizations. More definitions ...

Let $f: X \to Y$ be a proper morphism whose fibers have different dimensions, in particular $f$ is not flat. Let $L$ be a line bundle on $X$. What conditions would be sufficient to be able to conclude ...

Let $\mathcal{F}$ be a sheaf on the big etale site of $Sm_k$. I am looking for a way to calculate a modified version of sheaf cohomology. Let $X$ be a smooth scheme and $Z$ a closed sub-scheme. After ...

Let $f:X \to Y$ be a faithfully flat projective morphism of noetherial $\mathbb{C}$-schemes. Assume that $Y$ is affine, smooth over $\mathbb{C}$. Let $y \in Y$ be a closed point with residue field, ...