Project C2 lies at the juncture between representation theory of finite-dimensional algebras, non-commutative algebraic geometry and geometric group theory. Its goal is to study hereditary abelian categories over a non-algebraically closed field (and, more speculatively, hereditary exact categories) and use them to advance our understanding of quantised enveloping algebras, extended Weyl groups (such as elliptic groups of Saito) and extended Artin groups.