Given a topological space X, i'd like to find Der X - the derived category of sheaves of abelian groups on X - to be a closed monoidal category. Hom should be cohomological and the …

Consider a topos, i.e. the category $Shv$ of sheaves on a Grothendieck site $T$ with values in abelian groups. The category $Shv$ is symmetric monoidal with $\otimes$, the tensor p …

First, pick a commutative ring $k$ as the "ground field". Everything I say will be $k$-linear, e.g. "algebra" means "unital associative algebra over $k$". Then recall the followi …

On Pages 1-3 of Cours 2 of Toën's Master Course on Stacks, he defines the notion of a Geometric context with a rather extensive list of axioms (they take up about two pages over an …

Is there a notion (for schemes or just locally ringed spaces) of cohomology with compact support? I guess there is for algebraic schemes over $\mathbf{C}$, but what about schemes i …

Is there a description of of sheaf cohomology for the sheaf of sections of a continuous function in terms of common constructions in Algebraic Topology? In more detail: Any sheaf …

Hello everyone. My question is concerned with the following statement. "Having a grothendieck topology on a category C is equivalent to having a full reflective subcategory Sh(C) …

Given a $O_X$ module $\cal F$ whose support is a closed subscheme $Z \subset X$. Under what conditions can we say that $ \cal F$ is an $O_S$ module ( how far off is $\cal F$ an $O_ …

Take a smooth manifold $M^n$ with a smooth foliation $F$. Consider the sheaf $\cal F$ of $C^{\infty}$ functions on $M^n$, locally constant along the foliation $F$. What is known ab …

Given a topological space X we can define the sheaf cohomology of X in I. the Grothendieck style (as the right derived functor of the global sections functor Gamma(X,-)) or II. …

There are several theorems I know of the form "Let $X$ be a locally ringed space obeying some condition like existence of partitions of unity. Let $E$ be a sheaf of $\mathcal{O}_X$ …

Given a topological space X and a finite cover X = $\cup X_i$, one can define Cech cohomology of a sheaf of abelian groups F with respect to the cover ${X_i}$ in two different way …

There are two ways to define smooth mapping spaces and I want to know how they compare? Let's take the concrete special case of free loops spaces. I think this is the most studied …

Is there a relative version of sheaf cohomology? EDIT: I rather mean the cohomology of pairs.

This is a rather nice question I got from this user via private communication. Let $\mathcal{C} = Top$ the category of topological spaces. Let $\mathcal{C}^\prime$ be the category …