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arXiv · 2503.00911

Two characterizations of Bass orders via branches

Luis Arenas-Carmona
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Abstract

It has been known for some time that the orders in the four dimensional matrix algebra over a local field that can be written as a finite intersection of maximal orders are precisely those whose Gorenstein closure is Eichler. In this paper, a similar characterization is given for orders whose Gorenstein closure is a Bass order. A second characterization, this time for the Bass orders themselves, is given in terms of their branches, i.e., maximal subgraphs of the Bruhat-Tits tree whose vertices are orders containing them.

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Luis Arenas-Carmona. 2025-03-02. Two characterizations of Bass orders via branches. https://arxiv.org/abs/2503.00911

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