Tropical analytic geometry, Newton polygons, and tropical intersections
- 作者：Joseph Rabinoff rabinoff@post.harvard.edu
- 关键词：Tropical geometry ; Newton polygon ; Tropical intersection theory ; Non-Archimedean geometry
- 刊名：Advances in Mathematics
- 出版年：2012
- 期刊代码：62_00018708
- 类别：mt
- 出版时间：1 April, 2012
- 卷：229
- 期：6
- 页码：3192-3255
- 文件大小：599 K
摘要
In this paper we use the connections between tropical algebraic geometry and rigid-analytic geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in several variables: if are n convergent power series in n variables with coefficients in a non-Archimedean field K, we give a formula for the valuations and multiplicities of the common zeros of . We use rigid-analytic methods to show that stable complete intersections of tropical hypersurfaces compute algebraic multiplicities even when the intersection is not tropically proper. These results are naturally formulated and proved using the theory of tropicalizations of rigid-analytic spaces, as introduced by Einsiedler, Kapranov, and Lind (2006) and Gubler (2007) . We have written this paper to be as readable as possible both to tropical and arithmetic geometers.