Local universal lifting spaces of mod l Galois representations

Abstract

Let p and l be distinct primes, K a finite extension of Q(p), and (rho) over bar : Gal((K) over bar /K)-> GL(n),((F) over barl) a mod l Galois representation. In this paper, we show that the generic fiber of universal lifting space of (rho) over bar 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 rho's of (rho) over bar with unipotent rho vertical bar I-K's, when pi', is trivial or n <= 4 and the square of the order of the residue field of K is not equal to 1 mod l. (C) 2017 Elsevier Inc. All rights reserved.