域上赋值与序的链环不变量
Linking Invariants for Valuations and Orderings on Fields
AI总结：
该论文将Morishita的算术Milnor不变量理论从数域推广到一般域，引入离散赋值与序的链环不变量，并揭示其与Magnus同态系数及Galois上同调中Massey积的联系。
摘要：
由Morishita引入的模2算术Milnor不变量，为具有单位三角Galois群的$\mathbb{Q}$的典范Galois扩张中的素数提供了一种分解律，并将Legendre符号和Redei符号作为特例包含在内。Morishita进一步提出了模q算术Milnor不变量的概念，其中q为素数幂，适用于包含q次单位根且满足特定类域论假设的数域。我们将这一理论从数域背景推广到一般域，通过引入离散赋值与序的链环不变量的概念。我们进一步将其表示为Magnus同态系数，并将其与Galois上同调中的Massey积元素联系起来。
英文摘要：
The mod-2 arithmetic Milnor invariants, introduced by Morishita, provide a decomposition law for primes in canonical Galois extensions of $\mathbb{Q}$ with unitriangular Galois groups, and contain the Legendre and Redei symbols as special cases. Morishita further proposed a notion of mod-q arithmetic Milnor invariants, where q is a prime power, for number fields containing the q-th roots of unity and satisfying certain class field theory assumptions. We extend this theory from the number field context to general fields, by introducing a notion of a linking invariant for discrete valuations and orderings. We further express it as a Magnus homomorphism coefficient, and relate it to Massey product elements in Galois cohomology.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
