All Questions
Tagged with etale-covers schemes
7 questions
1
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211
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Characterize descents of geometric finite étale cover by means of homotopy exact sequence
Let $X/k$ be a geometrically connected $k$-variety (=separated of finite type, esp quasi-compact; the base field $k$ assumed to be separable, so $\overline{k}=k^{\text{sep}}$), $\overline{X} := X \...
- 6,038
2
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1
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94
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Base change for fundamental group prime to p in mixed characteristic?
I found the answer to this question while typing it up, but since I've already written it, it is probably worthwhile to post-and-answer in case someone finds it useful.
Let $S=\operatorname{Spec}\...
- 371
5
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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 ...
- 6,038
1
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Projection from closure of locally closed subscheme is Etale
Let $S$ an arbitrary scheme and denote by $\Delta: S \to S \times S$ the diagonal immersion and $p_i: S \times S \to S$ the both projections to first resp second factor. (in following we will wlog ...
- 6,038
10
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Are higher etale homotopy groups topological groups in a natural way?
Since etale fundamental group of a scheme $X$ is the group of natural automorphisms of the fibre functor of the category of finite etale covers of $X$, it comes with structure of a topological group. ...
- 723
3
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An Explicit Example of Galois Theory for Schemes
I'm currently attempting to understand Galois theory for schemes, largely following the books Galois Theory for Schemes by Henrik Lenstra and Galois Groups and Fundamental Groups by Tamas Szamuely. ...
user106566
0
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Artin approximation of a diagram
Let consider $f:(X,x)\to (Z,z)$ and $g:(Y,y)\to (Z,z)$ morphisms of pointed $k$-schemes of finite type ($k$ is a field). Suppose that there exists a map on the level of formal neighborhoods $\phi:X_{x}...
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