TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.369, no.8, pp.5425 - 5466
Abstract
Let p > 3 be a prime number and let GQ(p) be the absolute Galois group of Q(p). In this paper, we find Galois stable lattices in the 3-dimensional irreducible semi-stable non-crystalline representations of GQ(p) with Hodge-Tate weights (0, 1, 2) by constructing the corresponding strongly divisible modules. We also compute the Breuil modules corresponding to the mod p reductions of these strongly divisible modules and determine which of the original representations has an absolutely irreducible mod p reduction.