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arXiv · 1910.14450

On the closed subschemes of a scheme

Abolfazl Tarizadeh
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Abstract

In this paper, we obtain some new results on closed subschemes. Specially, we define natural addition and multiplication on the closed subschemes of a scheme. It is shown that "the multiplication" precisely coincides with the well known notion of "the scheme-theoretic intersection". Dually, "the addition" coincides with "the scheme-theoretic union". It is also proved that these structures naturally provide contravariant functors from the category of schemes to the category of commutative monoids.

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Abolfazl Tarizadeh. 2019-10-31. On the closed subschemes of a scheme. https://arxiv.org/abs/1910.14450

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