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4 votes
0 answers
97 views

Is there a concept of a map of Grothendieck sites having dense image?

Someone recently asked if one can talk about a map being etale dense just like one can talk about it being Zariski dense. My main question is: has anyone discussed such a notion? On a simple ...
David Corwin's user avatar
  • 15.4k
2 votes
0 answers
174 views

Finite étale morphism from a scheme to an algebraic space

Let $f : X \to Y$ be a finite, surjective étale morphism of algebraic spaces (say, of finite type over some noetherian scheme). Assume that $X$ is a scheme. Does this imply that $Y$ is a scheme? Is $Y$...
Mellon's user avatar
  • 197
5 votes
0 answers
349 views

Algebraic spaces as quotients of schemes (Definition from wikipedia)

I think that wikipedia article on Algebraic spaces contains a serious content error in the part on the definition of Algebraic spaces as quotients of schemes and I would like to discuss if it is ...
user267839's user avatar
  • 6,038
7 votes
1 answer
695 views

Constructible étale sheaves on X are étale algebraic spaces over X

I saw the following statement in a paper of Bhatt-Mathew: Let $X$ be a quasicompact quasiseparated scheme. Then there is an equivalence of categories between constructible étale sheaves (of sets) on ...
Steve's user avatar
  • 493