论文标题
使用Jacobian Vailitey的有限GALOIS扩展字段的互惠定律
Reciprocity law of finite Galois extension fields using Jacobian Varitey
论文作者
论文摘要
对于由代数整数环上的奇数不可还能多项式定义的有限galois扩展字段，我们通过将多项式的所有根嵌入雅各比式品种的2个tor仪点中，通过雅各布品种观察到“互惠法”。此外，该多项式的最小拆分场的Galois组是带有系数$ \ mathbb {f} _ {2} $的通用线性组的子组。
For finite Galois extension fields defined by odd degree irreducible polynomials over algebraic integer ring, we observe "Reciprocity Law" through Jacobian Variety by embedding all roots of the polynomials into 2-torsion points of Jacobian Variety. Furthermore, Galois group of the minimal splitting field of such a polynomial is a subgroup of general linear group with coefficient $\mathbb{F}_{2}$.
