Karl Schwede (Utah)

PDL C-38

Title: Test ideals for quasi-projective schemes in mixed characteristic

Abstract: Building on breakthrough results of Andr\'e, Bhatt, Gabber and others, Ma and the speaker introduced a theory of mixed characteristic test ideals / multiplier ideals. There was a gap in this theory, it was defined only for complete local rings and the formation of these ideals did not seem to commute with localization. By utilizing ideas from Bhatt-Ma-Patakfalvi-Tucker-Waldron-Witsazek and the author (also see Takamatsu-Yoshikawa), we introduce a notion of multiplier / test ideals for normal schemes finite type over a complete local ring (in particular our notion commutes with localization). We use our theory to study the non-nef locus and so obtain mixed characteristic versions of results on the non-nef locus for varieties over fields due to Ein-Lazarsfeld-Mustata-Nakamaye-Popa, Mustata, and Nakayama. This is joint work with Christopher Hacon and Alicia Lamarche.

The talk will be preceded with a pre-seminar starting at 2pm:

Title: Introduction to multiplier ideals and test ideals

Abstract: I'll give a brief introduction to multiplier ideals, what they are and how they measure singularities of algebraic varieties, and their connection to a positive characteristic construction called test ideals.

The talk will also be available via Zoom: https://washington.zoom.us/j/689897930

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