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On proper splinters in positive characteristic

Part of: Algebraic groups (Co)homology theory Arithmetic problems. Diophantine geometry Birational geometry Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  16 December 2025

Johannes Krah  and
Charles Vial Open the ORCID record for Charles Vial [Opens in a new window]
Johannes Krah
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany jkrah@math.uni-bielefeld.de
Charles Vial
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany vial@math.uni-bielefeld.de
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Abstract

While the splinter property is a local property for Noetherian schemes in characteristic zero, Bhatt observed that it imposes strong conditions on the global geometry of proper schemes in positive characteristic. We show that if a proper scheme over a field of positive characteristic is a splinter, then its Nori fundamental group scheme is trivial and its Kodaira dimension is negative. In another direction, Bhatt also showed that any splinter in positive characteristic is a derived splinter. We ask whether the splinter property is a derived invariant for projective varieties in positive characteristic and give a positive answer for normal Gorenstein projective varieties with big anticanonical divisor. We also show that global F-regularity is a derived invariant for normal Gorenstein projective varieties in positive characteristic.

Keywords

splintersglobally F-regular varietiesNori fundamental group schemederived equivalenceK-equivalenceexceptional inverse image functor

MSC classification

Primary: 14G17: Positive characteristic ground fields 14F35: Homotopy theory; fundamental groups 14L30: Group actions on varieties or schemes (quotients)
Secondary: 14J17: Singularities 14J26: Rational and ruled surfaces 14E05: Rational and birational maps

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Type
Research Article
Information
Compositio Mathematica , Volume 161 , Issue 10 , October 2025 , pp. 2493 - 2544
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Copyright
© The Author(s), 2025. The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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