Generic ordinarity for semi-stable fibration
Junmyeong Jang
TL;DR
This paper proves that semi-stable fibrations with ordinary generic fibers satisfy semi-positivity and constructs a counterexample to Parshin's conjecture on the Miyaoka-Yau inequality.
Contribution
It establishes a semi-positivity result for semi-stable fibrations with ordinary generic fibers and provides a counterexample to a longstanding conjecture.
Findings
Semi-positivity theorem holds for certain semi-stable fibrations.
Constructed a counterexample to Parshin's conjecture.
Shows the importance of ordinarity in geometric properties.
Abstract
In this paper, we proved that, for a semi-stable fibration of a proper smooth surface to a proper smooth curve over a field of positive characteristic, if the generic fiber is ordinary, then the semi-positivity theorem holds. As an application, we constrcuted a counterexample to Parshin's conjecture on the Miyaoka-Yau inequality.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows