Presheaf
Let $X$ be a topological space.A presheaf $A$ (of sets) on $X$ is a contravariant functor from the category of open subsets of $X$ and inclusions to t ...
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SheafLet $X$ be a topological space.A sheaf $\mathcal{F}$ of sets on $X$ is a presheaf of sets which satisfies the following additional property: Given any ...
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Locally ringed spacesA locally ringed spaces is a ringed space $(X, \mathcal{O}_ X)$ such that the stalks of $\mathcal{O}_ X$ are local rings. ...
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Ringed spacesA ringed space is a pair $(X, \mathcal{O}_ X)$ consisting of a topological space $X$ and a sheaf of rings $\mathcal{O}_ X$ on $X$. A morphism of ringe ...
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Number theoryNo description
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Convex rankLet $(\Gamma,\cdot,\leq)$ be an ordered abelian group. The convex rank of $\Gamma$ is the supremum of the length over chains of convex subgroups of $\ ...
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SchemesA scheme is a locally ringed space with the property that every point has an open neighbourhood which is an affine scheme. A morphism of schemes is a ...
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Valuation theoryNo description
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$p$-divisible groupsA $p$-divisible group is a tower of affine group schemes $$G_{1}\subset G_{2}\subset G_{3}\subset G_{4}\subset \cdot\cdot\cdot$$ such that some extra ...
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