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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A functor to ringed spaces

Author: Gail L. Carns
Journal: Proc. Amer. Math. Soc. 29 (1971), 222-228
MSC: Primary 18.20
MathSciNet review: 0276304
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Abstract: With the set of orders $ \mathcal{O}$ on a field and the Harrison topology induced from the set of all primes as a base space we define a ringed space $ (\mathcal{O},\mathcal{F})$. For each field homomorphism we find an associated ringed space morphism producing a contravariant functor from the category of fields to the category of ringed spaces. An equivalence relation $ \sim $ is defined on the set of orders and again a ringed space $ (\mathcal{O}/\sim, \bar{\mathcal{F}})$ and a contravariant functor from fields to ringed spaces is obtained along with a natural transformation from the first to the second functor. Finally, we obtain a ringed space morphism $ (\mathcal{O}/\sim, \bar{\mathcal{F}}) \to (Y, \mathcal{O}_Y)$ where Y is the spectrum of the ring of bounded elements and $ {\mathcal{O}_Y}$ is the structure sheaf.

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Keywords: Field, sheaf, ringed space, order, structure sheaf
Article copyright: © Copyright 1971 American Mathematical Society

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