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Results tagged with schemes
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user 5513
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
votes
Accepted
The restriction of a global section which is not a zero divisor is still a non-zero divisor?
Here's a counterexample.
Let $P=\mathbb{P}^1$, $X=\mathbb{A}^1$, and attach $X$ to $P$ along a single point $\{x\}$. Then there is a global section $f$ which is nonzero on $X$ except at $x$, and is i …
- 4,790
17
votes
Accepted
Is every regular (excellent) scheme separated?
- Separated, excellent, regular: Spec$(k)$.
- Separated, excellent, not regular: Spec$(k[\epsilon]/\epsilon^2)$.
- Separated, not excellent, regular: See http://en.wikipedia.org/wiki/Excellent_ring
…
- 4,790
11
votes
What are the epimorphisms in the category of schemes?
$\DeclareMathOperator\Spec{Spec}$Actually, your suggested categorical characterization of spectra of fields does work.
Edit: (I had written something incorrect here)
By Martin's comment below, we just …
- 4,790