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Results tagged with ag.algebraic-geometry
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user 128825
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
11
votes
Is $\operatorname{Spec}( \mathbb Q[x_1\ldots,x_n])$ simply connected space?
$\mathrm{Spec}(\mathbb{Q}[x_1,...,x_n])=\mathbb{A}^n_\mathbb{Q}$ is not étale simply connected as $\widehat{\pi}_1(\mathbb{A}^n_\mathbb{Q})=\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$, but $\mathr …
- 303
10
votes
Spec Z is simply connected space?
Here's a nice way to see that $\mathrm{Spec}(\mathbb{Z})$ is étale simply connected. Since $\mathrm{Spec}(\mathbb{Z})$ is a normal scheme every connected finite étale cover of $\mathrm{Spec}(\mathbb{Z …
- 303
5
votes
Accepted
What is the spectral interpretation of the arithmetic zeta function?
First, it's worth mentioning that the above theorem refers to the (local) Hasse-Weil zeta function of a scheme $X$ of finite type over $\mathbb{F}_q$ rather than the arithmetic zeta function of a sche …
- 303
3
votes
Galois categories for topological spaces?
To expand on Niels' answer: given a connected semilocally simply connected topological space $X$ and a point $x\in X$, the fiber functor $F_x:\mathrm{Cov}_X\rightarrow\mathrm{Set}$ from the category o …
- 303