TY - EJOUR
DO - 10.1016/j.jnt.2009.02.012
AB - Let K be a finite extension of Q(p), let L/K be a finite abelian Galois extension of odd degree and let D-L be the valuation ring of L. We define A(L/K) to be the unique fractional D-L-ideal with square equal to the inverse different of L/K. For p an odd prime and L/Q(p) contained in certain cyclotomic extensions, Erez has described integral normal bases for A(L)/Q(p) that are self-dual with respect to the trace form. Assuming K/Q(p) to be unramified we generate odd abelian weakly ramified extensions of K using Lubin-Tate formal groups. We then use Dwork's exponential power series to explicitly construct self-dual integral normal bases for the square-root of the inverse different in these extensions. (C) 2009 Elsevier Inc. All rights reserved.
T1 - Explicit construction of self-dual integral normal bases for the square-root of the inverse different
DA - 2009
AU - Pickett, Erik Jarl
JF - Journal Of Number Theory
SP - 1773-1785
VL - 129
EP - 1773-1785
ID - 159804
KW - Local field
KW - Galois module
KW - Self-dual
KW - Normal basis
KW - Lubin-Tate
KW - Formal group
KW - Inverse different
KW - Trace form
KW - Dwork's power series
KW - Extensions
KW - Forms
ER -