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Results tagged with schemes
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user 65846
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.
6
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Accepted
Motivation for Henselian rings in algebraic geometry
First about the ralation between henselian and formal smoothness property, I think a good idea is to look at what was the first version of Hensel lemma: it says that if $f(\bar{a})=0,f'(\bar{a})\, mo …
- 1,093
1
vote
Intuition behind formal neighborhood and local ring and formal power series
First of all $\mathbb{C[[x,y]]}$ is local because it is only depend on $\mathbb{C}[x,y]_{(x,y)}$ because by definition it is $lim \frac{\mathbb{C}[x,y]}{(X,Y)^n}$ and all things outside $(X,Y)$ are in …
- 1,093