Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers

• 成果类型: Article
• 署名作者: Ma, Linquan; Schwede, Karl
• 署名单位: Purdue University System; Purdue University; Utah System of Higher Education; University of Utah
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0813-1
• 发表日期: 2018
• 页码: 913-955
• 关键词: equivalence; topologies; VARIETIES; THEOREM

摘要

Using perfectoid algebras we introduce a mixed characteristic analog of the multiplier ideal, respectively test ideal, from characteristic zero, respectively in the case of a regular ambient ring. We prove several properties about this ideal such as subadditivity. We then use these techniques to derive a uniform bound on the growth of symbolic powers of radical ideals in all excellent regular rings. The analogous result was shown in equal characteristic by Ein-Lazarsfeld-Smith and Hochster-Huneke.