Journal of Noncommutative Geometry


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Volume 13, Issue 2, 2019, pp. 517–552
DOI: 10.4171/JNCG/329

Published online: 2019-07-17

An abstract characterization of noncommutative projective lines

Adam Nyman[1]

(1) Western Washington University, Bellingham, USA

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.

Keywords: Noncommutative algebraic geometry, noncommutative curve

Nyman Adam: An abstract characterization of noncommutative projective lines. J. Noncommut. Geom. 13 (2019), 517-552. doi: 10.4171/JNCG/329