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Results tagged with schemes
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user 31233
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.
1
vote
Affine communication lemma and finite limits in the category of rings
I think that Section 11 on transfer principles in these notes of mine is what you're looking for. A general machinery abstracts the business of tracking all the $f_i$'s and the required high powers. T …
- 3,312
9
votes
1
answer
326
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When are free modules on sheaves of sets quasicoherent?
This question was previously asked over at math.SE.
Let $X$ be a scheme. Let $\mathcal{E}$ be a sheaf of sets on $X$. Then we can define $\mathcal{O}_X\langle\mathcal{E}\rangle$, the free module over …
- 3,312
6
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Construction of the petit Zariski topos out of the gros topos of a scheme
Many of these toposes admit descriptions as internal classifying toposes, hence indeed enjoy useful universal properties. Here is a selection of such descriptions:
Constructing the big Zariski topos …
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