形式实赋值域的牛顿多边形法则及带符号热带超域上的重数
环与代数
2021-03-25 v2 交换代数
摘要
通过为超域上多项式的零点定义重数,Baker 与 Lorscheid 得以对 Descartes 符号法则与形式实赋值域上多项式的牛顿多边形法则提供统一的视角。在本文中,我们将他们的重数公式应用于与形式实赋值域相关的超域,以证明一条牛顿多边形法则,该法则将 Descartes 符号法则与经典牛顿多边形法则结合起来。
引用
@article{arxiv.1911.12274,
title = {A Newton Polygon Rule for Formally-Real Valued Fields and Multiplicities over the Signed Tropical Hyperfield},
author = {Trevor Gunn},
journal= {arXiv preprint arXiv:1911.12274},
year = {2021}
}
备注
16 pages, 2 figures, rephrased certain parts of the paper in terms of initial forms for consistency, added an example in the introduction, wrote some motivating exposition at the top of certain sections, definitions are now numbered, subsections 2.{5,6,7} are now a separate section (sec. 3), corrected some minor mistakes