Line bundles on rigid varieties and Hodge symmetry

Abstract

We prove several related results on the low-degree Hodge numbers of proper smooth rigid analytic varieties over non-archimedean fields. Our arguments rely on known structure theorems for the relevant Picard varieties, together with recent advances in p-adic Hodge theory. We also define a rigid analytic Albanese naturally associated with any smooth proper rigid space.

v1: 9 pages, comments welcome; v2: 8 pages, final and published version

References in corpus (1)

• On rigid varieties with projective reduction

Cited by in corpus (2)

• The $p$-adic Corlette-Simpson correspondence for abeloids
• Rigid-analytic varieties with projective reduction violating Hodge symmetry