All Questions

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 $S$ ...

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 ...

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 ...

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 ...

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 ...