Abstrakt
Suppose that kappa is lambda-supercompact witnessed by an elementary embedding j : V -> M with critical point kappa, and further suppose that F is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton's theorem: (1) for all alpha alpha kappa there is an elementary embedding j : V -> M with critical point kappa such that kappa is is closed under F, the model M is closed under lambda-sequences, H(F(lambda)) subset of M, and for each regular cardinal gamma {= lambda one has (vertical bar j(F)(gamma)vertical bar = F(gamma))(V), then there is a cardinal-preserving forcing extension in which 2(delta) = F(delta) for every regular cardinal delta and kappa remains lambda-supercornpact. This answers a question of [CM14].