Work

On the v-Picard Group of Stein Spaces

Year: 2024

Type: article

Abstract: We study the image of the Hodge–Tate logarithm map (in any cohomological degree), defined by Heuer, in the case of smooth Stein varieties. Heuer, motivated by the computations for the affine space of any dimension, raised the question whether this image is always equal to the group of closed differential forms. We show that it indeed always contains such forms but the quotient can be non-trivial: it contains a slightly mysterious $\mathbf{Z}_{p}$-module that maps, via the Bloch–Kato exponential map, to integral classes in the pro-étale cohomology. This quotient is already non-trivial for open unit disks of dimension strictly greater than $1$.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae185

Authors: Veronika Ertl, Sally Gilles, Wiesława Nizioł

Institutions: Institute of Mathematics, Institute for Advanced Study, Centre National de la Recherche Scientifique, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Research in Mathematics