Formal Structures and Representation Spaces

M. Kapranov introduced and studied in math.AG/9802041 the noncommutative formal structure of a smooth affine variety. In this note we show that his construction is a particular case of micro-localization and extend the construction functorially to representation schemes of affine algebras. We describe explicitly the formal completions in the case of path algebras of quivers and initiate the study of their finite dimensional representations.