General solution of corona problem

Our main result is a description of the spectrum of bidual algebra A^** of a uniform algebra A. This allows us to obtain abstract corona theorem for certain uniform algebras, asserting density of a specific Gleason part in the spectrum of an H^ -- type subalgebra of A^**. There is an isometric isomorphism of the latter subalgebra with H^ (G) for a wide class of domains G Cᵈ. Using abstract corona theorem we show the density of the canonical image of G in the spectrum of H^ (G), solving positively corona problem for this class (which in particular includes balls and polydisks).