An analogue of adjoint ideals and PLT singularities in mixed characteristic
| Autor: | Linquan Ma, Karl Schwede, Kevin Tucker, Joe Waldron, Jakub Witaszek |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Algebraic Geometry. 31:497-559 |
| ISSN: | 1534-7486 1056-3911 |
| DOI: | 10.1090/jag/797 |
| Popis: | We use the framework of perfectoid big Cohen-Macaulay (BCM) algebras to define a class of singularities for pairs in mixed characteristic, which we call purely BCM-regular singularities, and a corresponding adjoint ideal. We prove that these satisfy adjunction and inversion of adjunction with respect to the notion of BCM-regularity and the BCM test ideal defined by the first two authors. We compare them with the existing equal characteristic purely log terminal (PLT) and purely F F -regular singularities and adjoint ideals. As an application, we obtain a uniform version of the Briançon-Skoda theorem in mixed characteristic. We also use our theory to prove that two-dimensional Kawamata log terminal singularities are BCM-regular if the residue characteristic p > 5 p>5 , which implies an inversion of adjunction for three-dimensional PLT pairs of residue characteristic p > 5 p>5 . In particular, divisorial centers of PLT pairs in dimension three are normal when p > 5 p > 5 . Furthermore, in Appendix A we provide a streamlined construction of perfectoid big Cohen-Macaulay algebras and show new functoriality properties for them using the perfectoidization functor of Bhatt and Scholze. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|