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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



On rigid varieties with projective reduction

Author: Shizhang Li
Journal: J. Algebraic Geom. 29 (2020), 669-690
Published electronically: November 4, 2019
MathSciNet review: 4158462
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Abstract | References | Additional Information

Abstract: In this paper, we study smooth proper rigid varieties which admit formal models whose special fibers are projective. The Main Theorem asserts that the identity components of the associated rigid Picard varieties will automatically be proper. Consequently, we prove that $p$-adic Hopf varieties will never have a projective reduction. The proof of our Main Theorem uses the theory of moduli of semistable coherent sheaves.

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Additional Information

Shizhang Li
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027

Received by editor(s): November 8, 2018
Received by editor(s) in revised form: January 11, 2019
Published electronically: November 4, 2019
Article copyright: © Copyright 2019 University Press, Inc.