All Questions

In this question I'd like to examine some properties of universally closed morphisms. The question is self-contained. It can also be seen as a follow-up to this question. Let $R$ be a discrete ...

As a beginner who just get in touch with Euler characteristics in this field, could I get some intuition for the arithmetic meaning of Euler characteristics of bounded complexes, for example Selmer ...

Let $f : \mathcal{C}\to\mathcal{D}$ be a morphism of sites (see the Stacks Project) with induced morphism of topoi $$(f^{-1}, f_*) : Sh(\mathcal{D})\to Sh(\mathcal{C}).$$ By assumption, $f^{-1}$ is an ...

Milne, Étale Cohomology, theorem 8.5 states the following version of the Künneth formula (in slightly greater generality). Let $\Lambda$ be a finite commutative ring. Let $X, Y, S$ be schemes with $S$ ...

Motivated by an étale cohomology calculation I am going to do, here is a question that should have positive and not too hard answer. Let $A$ be a ring, $A_0$ a ring such that $A_0$ is equipped with ...

Let $X$ be a smooth projective variety over a field. Is $$H^p(X_{Zar},\mathbf{G}_a\otimes_{\mathbf{Z}}\mathbf{G}_a)$$ at all related to $H^p(X_{Zar},\mathbf{G}_a) = H^p(X,\mathcal{O}_X)$ via tensor ...