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arXiv · 1506.04890

On integral schemes over symmetric monoidal categories

Abhishek Banerjee
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Abstract

We propose notions of "Noetherian" and "integral" for schemes over an abelian symmetric monoidal category $(\mathcal C,\otimes,1)$. For Noetherian integral schemes, we construct a "function field" that is a commutative monoid object of $(\mathcal C,\otimes,1)$. Under certain conditions, we show that a Noetherian scheme over $(\mathcal C,\otimes,1)$ is integral if and only if it is reduced and irreducible.

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Abhishek Banerjee. 2015-06-16. On integral schemes over symmetric monoidal categories. https://arxiv.org/abs/1506.04890

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