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Results tagged with ag.algebraic-geometry
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user 35575
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
13
votes
Does $\pi_1(Spec(\mathbb{Z}[1/p]))$ depend on p?
To add on to Pete's answer, let me comment that the differences are even more pronounced if we look at the maximal pro-$p$ quotient $\pi_1(\operatorname{Spec}(\mathbb{Z}\left[\frac{1}{p_1p_2\cdots p_r …
- 8,467
17
votes
Conceptualizing Weil Pairing for elliptic curves ( and number fields)
The unifying picture you're looking for is probably most transparent the other way around -- by re-writing the Weil pairing on elliptic curves (in fact, this works more generally for Jacobians) to mak …
- 8,467
17
votes
Questions about analogy between Spec Z and 3-manifolds
This has been well-addressed by the answerers before me, but just to chime in -- there are a variety of analogs one could make for the Poincare conjecture for number fields. For one, there are severa …
- 8,467
5
votes
Accepted
Etale coverings of certain open subschemes in Spec O_K
As Kevin points out, $V$ is indeed $\mathcal{O}_K[\frac{1}{2}]$ in your example. Your link to the fundamental group is also correct. $\pi_1(U)$ is the Galois group of the maximal extension of $\math …
- 8,467
7
votes
On what kind of objects do the Galois groups act?
This is not exactly an incarnation of the question you asked, in the sense that is not so much an action of a Galois group but rather an action whose existence is governed by a Galois group of number- …
- 8,467