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Results tagged with schemes
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user 43054
The first purpose of schemes theory is the geometrical study of solutions of algebraic systems of equations, not only over the real/complex numbers, but also over integer numbers (and more generally over any commutative ring with 1). It was finalized by Alexandre Grothendieck, during the 1950s and the 1960s.
4
votes
Why geometric generic point (in abstract algebraic geometry) replace general points in the u...
If you want a canonical description of the homotopy type of the general fiber, you can take the homotopy type of the space $X\times_{\mathbb{D}}\mathbb{H}$ where $\mathbb{H}:=\{z\in\mathbb{C}\mid \Im …
- 16.5k
10
votes
Irreducible of finite Krull dimension implies quasi-compact?
The answer is no for all these questions. Take the line with infinite origins: the scheme obtained by gluing an infinite amount of copies of $\mathbb{A}^1$ along the open subsets $\mathbb{G}_m$. This …
- 16.5k
18
votes
Accepted
Are higher etale homotopy groups topological groups in a natural way?
If you choose to see profinite groups as topological groups, group schemes or pro-systems is largely a matter of choice.
How is the étale homotopy group defined? …
- 16.5k
15
votes
An apparent equivalence of the category of affine schemes over $S$ and the category of quasi...
What is true is that there is an antiequivalence between the category of schemes affine over $S$ (that is $S$-schemes for which the preimage of an open affine of $S$ is an open affine) and quasi-coherent …
- 16.5k