On rigid varieties with projective reduction

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 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.