  Let k be a perfect field and let K/k be a finite extension of fields. An
arithmetic noncommutative projective line is a noncommutative space equal to
the projectivization of the noncommutative symmetric algebra of a k-central two
-sided vector space of rank two over K. We study the geometry of these spaces.
More precisely, we prove they are integral, we classify vector bundles over
them, we classify them up to isomorphism, and we classify isomorphisms between
them. Using the classification of isomorphisms, we compute the automorphism
group of an arithmetic noncommutative projective line.
