The scheme of characters in sl2

The aim of this article is to study the SL2(C)-character scheme of a finitely generated group. Given a presentation of a finitely generated group I', we give equations defining the coordinate ring of the scheme of SL2(C)- characters of I' (finitely many equations when I' is finitely presented). We also study the scheme of abelian and non-simple representations and characters. Finally we apply our results to study the SL2(C)-character scheme of the Borromean rings.