Witt's theorem for noncommutative conics

TL;DR

This paper generalizes Witt's theorem to noncommutative conics by classifying homogeneous noncommutative genus zero curves as noncommutative P^1-bundles and computing their invariants.

Contribution

It extends Witt's theorem to noncommutative geometry by classifying noncommutative genus zero curves and determining their isomorphism invariants.

Findings

Homogeneous noncommutative genus zero curves are noncommutative P^1-bundles.

Complete isomorphism invariants for these curves are computed.

Generalization of Witt's theorem to noncommutative conics.

Abstract

Let k be a field. We show that all homogeneous noncommutative curves of genus zero over k are noncommutative P^1-bundles over a (possibly) noncommutative base. Using this result, we compute complete isomorphism invariants of homogeneous noncommutative curves of genus zero, allowing us to generalize a theorem of Witt.