English

On integral schemes over symmetric monoidal categories

Algebraic Geometry 2016-05-17 v2

Abstract

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

Keywords

Cite

@article{arxiv.1506.04890,
  title  = {On integral schemes over symmetric monoidal categories},
  author = {Abhishek Banerjee},
  journal= {arXiv preprint arXiv:1506.04890},
  year   = {2016}
}

Comments

One result added from previous version. This paper will not be published in its present form. The results and methods herein will be subsumed into two further papers

R2 v1 2026-06-22T09:54:22.551Z