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
DOI: https://doi.org/10.1090/jag/740
Published electronically: November 4, 2019
Full-text PDF

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.


References [Enhancements On Off] (What's this?)


Additional Information

Shizhang Li
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: shizhang@umich.edu

DOI: https://doi.org/10.1090/jag/740
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.