Q: Is there a simple proof of the fact that the Weil restriction of an abelian scheme along a finite étale morphism is an abelian scheme ? Details: Let $S$ be a scheme and $f:S'\r …

Let $X$ be a (reasonable) scheme. I'm curious about constructing the constructing the covering space of a scheme algebraically. The covering space functor $F$ (below) can be repres …

My question concerns morphisms between algebraic spaces. I like the definitions of Artin, but I do not see a simple proof of the fact that the composition of two morphisms is a mor …

In this MO question it is claimed that a catchphrase for "algebraic spaces" could be that they are "the result of looking at the orbit space of the action of a finite group on a sc …

I have a technical question coming from reading Toen's master course on stacks. If we view schemes as locally ringed spaces then there we could define a morphism to be surjective …

Suppose G is a group object in the category of algebraic spaces (over a field, if you like, or even over ℂ if you really want). Is G necessarily a scheme? My feeling is that …

Suppose $F:Sch^\text{op}\to Set$ is a sheaf in the fpqc topology, has quasi-compact representable diagonal, and has an fpqc cover by a scheme. Must $F$ be an algebraic space? Th …

Let $S$ be a scheme and let $N$, $G$ be affine flat group schemes of finite presentation over $S$. If we assume that $N$ is a closed normal subgroup of $G$, we may form the fppf qu …

The answer to the following question is probably well known or the question itself is well known not to have a reasonable answer. In the latter case could you please let me know wh …

Let $X$ be a proper smooth algebraic space over $\mathbb C$ (which amounts, due to Artin, to giving a Moishezon space: a compact complex manifold whose dimension equals the transce …

This question is related to the following question which I've just seen which was posted by Anton. His question is whether a algebraic space which is a group object is necessarily …

Let $f \colon X \to S$ be a proper morphism form a seperated algebraic space $X$ to an affine noetherian scheme $S$. Given a coherent sheaf $F$ on $X$, we know from Knutson's book …

I'm reading Knutson's book on algebraic spaces, and I stumbled over the quasi-separatedness axiom in his definition of algebraic spaces (Definition 1.1, Chapter II). He defines an …

Here's the context for the question: Proposition 4.6 of Freitag and Kiehl's book on etale cohomology shows that a sheaf (of sets) $\mathcal{F}$ (on the site Et(X)) is constructibl …

Let $R \rightrightarrows U \to X$ be a presentation of an algebraic space by schemes. Does this induce an exact sequence $|R| \rightrightarrows |U| \to |X|$ on underlying points? …