Pickett, Erik Jarl
Explicit construction of self-dual integral normal bases for the square-root of the inverse different
Journal Of Number Theory
10.1016/j.jnt.2009.02.012
129
1773-1785
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.
Local field;
Galois module;
Self-dual;
Normal basis;
Lubin-Tate;
Formal group;
Inverse different;
Trace form;
Dwork's power series;
Extensions;
Forms;
2009