厄米特函数域的格
Lattices from Hermitian function fields
摘要：
我们考虑著名的Rosenbloom-Tsfasman函数场格在厄米函数场的特殊情况下。我们证明了在这种情况下所得到的格是由它们的极小向量生成的，提供了对极小向量总数的估计，并导出了这些格的自同构群的性质。我们的研究是对椭圆曲线和有限阿贝尔群上的格的研究的继续。我们在这里所面临的格是更微妙的比以前考虑的，和证明的主要结果需要更换现有的线性代数的方法由深刻的结果格哈德希斯因式分解的功能与特定的除数支持线和他们的逆。
英文摘要：
We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the total number of minimal vectors, and derive properties of the automorphism groups of these lattices. Our study continues previous investigations of lattices coming from elliptic curves and finite Abelian groups. The lattices we are faced with here are more subtle than those considered previously, and the proofs of the main results require the replacement of the existing linear algebra approaches by deep results of Gerhard Hiss on the factorization of functions with particular divisor support into lines and their inverses.
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