| Let K be a finite extension of Qp , and let rho : Gal(K/K ) → GLn( Fp ) be a mod l Galois representation. If l ≠ p, we show that the generic fiber of universal lifting spaces of r&d1; is equidimensional, and we prove that the dimension of the generic fiber is n2. We show that the study of the universal lifting spaces of any r&d1; can be reduced to the study of the universal lifting spaces of Galois representations r&d1; which is trivial on the subgroup of the inertia group I K of Gal(K/K ) whose order is prime to l. Then we characterize the unipotent irreducible components of characteristic 0 for some special cases, especially when n ≤ 4 and the order of the residue field of K is not equal to 1 mod l. The only assumption I make is that the image of the lift of the Frobenius is semisimple. |
