All Questions

For integral schemes, the Picard group is isomorphic to the group of Cartier divisors modulo linear equivalence. What is the correct analog of this isomorphism, for higher codimension Chow groups vs ...

Let $X$ be a smooth projective variety over the complex numbers, and $\mathbf{Z}(p)_{\mathcal{D}}$ the Deligne complex on $X$: $$\mathbf{Z}(p)_{\mathcal{D}} : \ \ \mathbf{Z}(p)\to\mathcal{O}_X\to\...

Let $X$ be a quasi-projective variety over a perfect field $k$. Given a projective embedding $j : X\to \mathbf{P}(\mathscr{E})$, the Chow variety $\text{Chow}_r(X, j)$ is a quasi-projective variety ...

Let $X$ be a smooth variety over a field. Is there a spectral sequence: $$E_1^{p,q} := \bigoplus_{x\in X^{(p)}}H^{q-p}(\kappa(x)_{\rm ét},\mathbf{Z}(n))\Rightarrow H^{q-p}(X_{\rm ét},\mathbf{Z}(n))$$...

Is there an example of a smooth projective variety $X$ over the complex numbers, such that $$\ker(\text{CH}^2(X)\to H^4(X,\mathbf{Z}(2))$$ is not torsion?

Let $X$ be a smooth projective complex variety. Calling $f : X_{\rm an}\to X_{\rm Zar}$ the "change-of-topology" morphism of sites induced by sending a Zariski open $U$ of $X$ to its analytification, ...