LAUSR

Abstract Let p and l be distinct primes, K a finite extension of Q p , and ρ ‾ : Gal ( K ‾ / K ) → GL n ( F ‾ l ) a mod l Galois representation. In this paper, we show that the generic fiber of universal lifting space of ρ ‾ is equidimensional of dimension n 2 . We also characterize the irreducible components of the generic fiber of the universal lifting space which represent the liftings ρ's of ρ ‾ with unipotent ρ | I K 's, when ρ ‾ | I K is trivial or n ≤ 4 and the square of the order of the residue field of K is not equal to 1 mod l.