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On integral schemes over symmetric monoidal categories (1506.04890v2)
Published 16 Jun 2015 in math.AG
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.