Oct 18 2021

Algebraic Geometry Seminar: Test ideals for quasi-projective schemes in mixed characteristic, by Karl Schwede

October 18, 2021

3:00 PM - 3:50 PM




Chicago, IL

Karl Schwede (University of Utah): Test ideals for quasi-projective schemes in mixed characteristic

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.

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Kevin Tucker

Date posted

Oct 24, 2021

Date updated

Oct 24, 2021


Karl Schwede | (University of Utah)