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arXiv · 1704.04544

An abstract characterization of noncommutative projective lines

A. Nyman
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Abstract

Let $k$ be a field. We describe necessary and sufficient conditions for a $k$-linear abelian category to be a noncommutative projective line, i.e. a noncommutative $\mathbb{P}^{1}$-bundle over a pair of division rings over $k$. As an application, we prove that $\mathbb{P}^{1}_{n}$, Piontkovski's $n$th noncommutative projective line, is the noncommutative projectivization of an $n$-dimensional vector space.

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A. Nyman. 2017-04-14. An abstract characterization of noncommutative projective lines. https://arxiv.org/abs/1704.04544

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