On the compactification of Witt group schemes and the deformation of Art theory

论维特群方案的紧化与艺术理论的变形

• 批准号: 11640045
• 负责人: SEKIGUCHI Tsutomu
• 金额: $ 2.24万
• 依托单位: Chuo University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640045/
• 关键词: group scheme; Kummer theory; Artin-Scheme-Witt theory; Witt vector; Artin-hasse exponential series; extension of group schemes; Cartier module; Arti-Hasse指数関数; Canties加群; 群スキームの変形

Already we have showed the existence of group schemes which gave the deformations of the group schemes of Witt vectors to tori. Using those group schemes we could contract the unified Kummer-Artin-Schreier-Witt theory. But, when we want to apply the theory to some problems, for example, the lifting problem of cyclic coverings of algebraic curves, partially solved by Green-Matignon, we need more explict description of the group schemes. In 1999 and 2000, we devoted ourselves to construct concretely the group schemes giving the deformations of the group schemes of Witt vectors to tori, and we succeeded to descrive such group schemes by using several Witt vectors. In the background, there is the Cartier thory, and our thory is given by the representation of that by virtue of deformed Artin-Hasse exponential series.To descrive the ramifications of cyclic coverings, we need to compactfy such group schemes. In positive characteristic case. Garuti gave a nice compactifications of group schemes of Witt vectors by means of ruled surfaces. We tried to give compactifications of the deformed group schemes also, even it is in two-dimensional case, and we are on the way to investigate the description of ramification locuses geometrically.

我们已经展示了群体方案的存在，这些方案将Witt Vectors的组方案的变形与Tori的变形。使用这些小组计划，我们可以签订统一的Kummer-Artin-Schreier-Witt理论。但是，当我们想将理论应用到一些问题上时，例如，绿色 - 马蒂尼翁（Green-Matignon）部分解决了代数曲线的循环覆盖物的提升问题，我们需要对组方案的更多解释描述。在1999年和2000年，我们致力于构建群体方案，将Witt Vectors的小组方案变形为Tori，我们成功地通过使用多个Witt Vectors来描述此类群体方案。在背景中，有卡地亚（Cartier）thory，而我们的thory是通过变形的artin-hasse指数序列来给出的。在积极的特征情况下。 Garuti通过统治的表面很好地完成了Witt矢量的小组计划。我们也试图给出变形组方案的压缩，即使在二维情况下，我们也在几何上研究Ramifience Locuses的描述。

项目成果

T. Sekiguchi & N. Suwa: "A note on extensions of algebraic and formal groups V"(Preprint). (2001)

T·关口

T. Sekiguchi & N. Suwa: "On the unified Kummer-Artin-Schreier- Witt theory"Mathematiques Pures de Bordeaux C.N.R.S., Prepublication. n^0 111. 1-90 (1999)

T·关口

Tsutomu Sekiguchi: "A note on extensions of algebraie and formal groups, V"Preprint. 1-58 (2001)

Tsutomu Sekiguchi：“关于代数和形式群的扩展的注释，V”预印本。

Tsutomu Sekiguchi: "On the unified Kummer-Artin-Schreier-Witt theory"Mathematiques Pures de Bordeaux C.N.R.S., Prepublication. 111. 1-90 (1999)

Tsutomu Sekiguchi：“论统一的 Kummer-Artin-Schreier-Witt 理论”Mathematiques Pures de Bordeaux C.N.R.S.，预出版。

関口 力: "Jacobi多様体のSerre-Tate cavonical liftingについて"「暗号理論とそれを支える代数曲線」第2回ワークショップ報告集. 2. 5-12 (2001)

Riki Sekiguchi：“关于雅可比流形的 Serre-Tate 空洞提升”第二届密码学理论和支持它的代数曲线研讨会的报告 2. 5-12 (2001)。