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Results tagged with schemes
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user 157954
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.
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Subschemes of the affine line over a domain
Let $R$ be a domain with affine spectrum $S$ and consider the scheme $X=\mathbb A^1_R=\operatorname {Spec}R[T] $ over $S$.
Let $P\subset R[T]$ be an ideal with $P\cap R=0$ and let $Y\subset X$ be the …
- 417
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answer
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What are the sections of an ideal sheaf on a scheme?
Suppose $X$ is a scheme and $f_1,...,f_n\in \Gamma(X,\mathcal O)$ are global sections.
One often reads about the ideal sheaf $\mathcal I=\mathcal (f_1,...,f_n)\subset \mathcal O$, but I have never see …
- 417
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On the definition of a principal ideal sheaf
In his book Algebraic Geometry and Arithmetic Curves Qing Liu claims in Exercise 3.4, page 56, the following for a scheme $X$ and a global function $f\in \mathcal O_X(X)$:
"The map $U\mapsto f\vert _ …
- 417