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Reduced normal form of local integral bases

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 crutial property for several important applications. Except for very particular cases, a basis in Hermite normal form cannot be reduced.

preprint2016arXivOpen access
Nathália Moraes de OliveiraEnric Nart
math.NT
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Nathália Moraes de OliveiraEnric Nart

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