2017/05/31 by Linquan Ma, Karl Schwede · 1 citation
Mathematics · #math.AC #math.AG #msc:13B99 #msc:13A35 #msc:13D22 #msc:14F18 #msc:14B05 #msc:13D45 #msc:14B15
paper · pdf · doi:10.1007/s00222-018-0813-1
published as Invent. Math. 214 (2018), no. 2, 913-955 · 35 pages, numerous clarified proofs and expositional improvements throughout. To appear in Inventiones Mathematicae
arxiv created 2018/07/28 · arxiv updated 2019/06/25
Using perfectoid algebras, we introduce a mixed characteristic analog of the multiplier ideal, respectively test ideal, from characteristic zero, respectively p > 0, 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.