We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong σ-Gröbner bases. Moreover, we prove that the Terao's conjecture over finite fields implies the conjecture over the rationals.

中文翻译：

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组合等效的超平面布置

我们研究任意领域上的超平面布置的组合学。具体来说，我们通过使用最小的强σ- Gröbner基来确定在哪种情况下其质数的排列及其归约模具有同构晶格。此外，我们证明了Terao在有限域上的猜想隐含了在有理数上的猜想。