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Title: Lifts of Twisted K3 Surfaces to Characteristic 0
Abstract Deligne [9] showed that every K3 surface over an algebraically closed field of positive characteristic admits a lift to characteristic 0. We show the same is true for a twisted K3 surface. To do this, we study the versal deformation spaces of twisted K3 surfaces, which are particularly interesting when the characteristic divides the order of the Brauer class. We also give an algebraic construction of certain moduli spaces of twisted K3 surfaces over $${\operatorname {Spec}}\ \textbf {Z}$$ and apply our deformation theory to study their geometry. As an application of our results, we show that every derived equivalence between twisted K3 surfaces in positive characteristic is orientation preserving.  more » « less
Award ID(s):
1902875
PAR ID:
10553103
Author(s) / Creator(s):
Publisher / Repository:
International Mathematics Research Notices
Date Published:
Journal Name:
International Mathematics Research Notices
Volume:
2023
Issue:
5
ISSN:
1073-7928
Page Range / eLocation ID:
4337 to 4407
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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