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Results tagged with schemes
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user 118688
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.
3
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answers
150
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Other interesting notions when we change topology on $\text{Sch}/S$
Let $\text{Sch}$ be the category of schemes. Let $S$ be an object of $\text{Sch}$. Consider the category $\text{Sch}/S$. …
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1
vote
0
answers
92
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Topological space modeled by special topological structures
Let $X$ be a topological space. Suppose it is "modeled by" topological spaces of the form $\text{Spec}(A)$ for some commutative ring $A$, then, (along with some other conditions/structure), we call $ …
- 6,023
3
votes
1
answer
265
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"Covering-flat" part in definition of morphism of sites
Let $(\mathcal{C},\mathcal{I})$ and $(\mathcal{D},\mathcal{J})$ be sites where $\mathcal{C}, \mathcal{D}$ are categories and $\mathcal{I}$ and $\mathcal{J}$ are Grothendieck topologies on $\mathcal{C …
- 6,023
2
votes
1
answer
663
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Why care about Grothendieck topology? [closed]
Well, the original motivation (to my
understanding) was to develop a notion of etale cohomology for
schemes; so if you care about schemes, you should care about sites. … Question : In what sense does Grothendieck topologies are in relation with Etale cohomology of Schemes? …
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3
votes
1
answer
987
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Diagonal is representable then any morphism is representable
A stack $\mathcal{X}$ over a scheme $T$ is a stack over category "schemes over $T$" i.e., we have a functor $\mathcal{X}\rightarrow Sch/T$. …
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3
votes
0
answers
762
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Road map for moduli space/moduli problem/moduli stack
I am also comfortable with basics of Schemes, their Cohomology (Cech), from Hartshorne's Algebraic geometry. …
- 6,023