Reduced normal form of local integral bases
Volume 178 / 2017
Acta Arithmetica 178 (2017), 181-200
MSC: Primary 11R04; Secondary 11Y40.
DOI: 10.4064/aa8509-10-2016
Published online: 29 March 2017
Abstract
We introduce a canonical form for reduced bases of integral closures of discrete valuation rings, and we describe an algorithm for computing a basis in reduced normal form. This normal form has the same applications as the Hermite normal form: identification of isomorphic objects, construction of global bases by patching local ones, etc., but in addition the bases are reduced, which is a crucial property for several important applications. Except for very particular cases, a basis in Hermite normal form cannot be reduced.
