Let $E$ be your favorite elliptic curve, and let $Tor^m$ be the moduli stack of torsion sheaves of degree $m$ on $E$. This sounds horrible, but it's not so bad; it's a global quot …

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 …

Hello, I am looking for a reference (if it exists) that makes the link between cohomology of sheaves for sites and Galois cohomology : quickly said, I would like to see Galois c …

Suppose M is an arbitrary smooth manifold and D is its bundle of 1-densities. On the category of finite-dimensional vector bundles over M and linear differential operators between …

I am wondering if there is a more "geometric" formulation of complex orientations for cohomology theories than just a computation of $E^*\mathbb{C}$P$^{\infty}$ or a statement abou …

Suppose that we are given a smooth projective variety $X$ with a full exceptional collection of vector bundles $(F_1, F_2, \ldots, F_k)$ in $D^b(X)$ and two vector bundles $E_1$, $ …

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 …

For cohomology with coefficients in a field $F$ the map $H^\cdot(X;F) \otimes H^\cdot(Y;F) \to H^\cdot(X \times Y;F)$ of the Kunneth theorem is an isomorphism of algebras over $F$. …

In complex projective geometry, we have a specified Kähler class $\omega$ and we have a Lefschetz operator $L:H^i(X,\mathbb{C})\to H^{i+2}(X,\mathbb{C})$ given by $L(\eta)=\omega\w …

In question #7656, Peter Arndt asked why the Gamma function completes the Riemann zeta function in the sense that it makes the functional equation easy to write down. Several of t …

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 $\mathcal{O}_X$ …

I was looking through my notes for a homotopy theory course and found the following mysterious statement (K is of course the Eilenberg-Maclane space): $$H^{n+1}(K(\mathbb Z_p,n); …

Nakajima defined a while back a nice family of varieties, called "quiver varieties" (sometimes with "Nakajima" appended to the front to avoid confusion with other varieties defined …

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 …

So, let's say one has an action of $GL_n$ on an algebraic variety $X$ over a field $k$, and two objects $F,G$ in the equivariant derived category (i.e., the derived category of con …