  Poizat's construction of theories of fields with a multiplicative subgroup of
green points is extended in several directions: First, we also construct
similar theories where the green points form a divisible
$\operatorname{End}(E)$-submodule of an elliptic curve $E$. Second, the
subgroup (submodule) of green points is allowed to have torsion, whereas in
Poizat's work this more general case was only dealt with assuming the unproven
Conjecture on Intersections with Tori (CIT). Third, motivated by Zilber's work
on connections with non-commutative geometry, we construct a version of the
theories of green points in the multiplicative group case for which the
distinguished subgroup is not divisible but a $\mathbb{Z}$-group, which we call
theories of emerald points. In a subsequent joint paper with Boris Zilber we
find natural models for the constructed theories.
