  In constructive algebra one cannot in general decide the irreducibility of a
polynomial over a field K. This poses some problems to showing the existence of
the algebraic closure of K. We give a possible constructive interpretation of
the existence of the algebraic closure of a field in characteristic 0 by
building, in a constructive metatheory, a suitable site model where there is
such an algebraic closure. One can then extract computational content from this
model. We give examples of computation based on this model.
