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Reduced normal form of local integral bases

Volume 178 / 2017

Nathália Moraes de Oliveira, Enric Nart 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.

Authors

  • Nathália Moraes de OliveiraDepartament de Matemàtiques
    Universitat Autónoma de Barcelona
    Edifici C
    E-08193 Bellaterra, Barcelona, Catalonia, Spain
    e-mail
  • Enric NartDepartament de Matemàtiques
    Universitat Autónoma de Barcelona
    Edifici C
    E-08193 Bellaterra, Barcelona, Catalonia, Spain
    e-mail

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