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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.
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
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
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