Abstract :
Let (T, M) be a complete regular local ring of dimension at least 2, containing the rationals, such that the cardinality of the residue fieldT/Mis at least the cardinality of the real numbers. Supposep ≠ Mis a prime ideal ofT. We construct an excellent regular local ringAsuch that the completion ofAisTand the generic formal fiber ofAis local (this means that the ringT AKis a local ring whereKis the quotient field ofA) withp A Kits maximal ideal. In addition, ifqis a prime ideal ofTwithq ∩ A = P ≠ (0), thenq = PT.
