On the computation of overorders

2019/09/24 by Hofmann, Tommy, Sircana, Carlo · 1 citation
#11R04 #11Y40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1909.10860

Abstract

The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consider the related problems of computing all minimal overorders as well as all overorders of a given order. We use techniques from algorithmic representation theory and the theory of minimal integral ring extensions to obtain efficient and practical algorithms, whose implementation is publicly available.

Cited by

• Isogeny graphs of abelian varieties and singular ideals in orders

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• Generators of maximal orders
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