Algorithmic methods for arithmetic surfaces and regular, minimal models

算术曲面和常规最小模型的算法方法

• 批准号: 171586250
• 负责人: Professorin Dr. Anne Frühbis-Krüger
• 金额: --
• 依托单位: Institut für Mathematik (IFM)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/171586250?language=en
• 关键词: Algorithmic; methods; arithmetic; surfaces; regular

Regular and minimal models of algebraic curves over number fields are arithmetic surfaces that play an important role in arithmetic geometry. This research project aims at developing algorithms for such arithmetic surfaces and for the computation of regular and minimal models. The main topics are a desingularisation procedure following Lipman, functionality for the intersection pairing, exceptional divisors, blow ups and blow downs. On the basis of these algorithms applications to the Birch and Swinnerton-Dyer conjecture and other related areas are finally investigated.

数域上代数曲线的正则和极小模型是算术曲面，在算术几何中起着重要的作用。本研究项目的目的是开发算法，这样的算术表面和计算的规则和最小的模型。主要议题是一个desingularisation程序以下李普曼，功能的交叉配对，例外的除数，吹起来和吹唐斯。在此基础上，研究了这些算法在Birch猜想和Swinnerton-Dyer猜想等相关领域中的应用。