Notes on a p-adic exponential map for the Picard group
Algebraic Geometry
2017-01-27 v2
Abstract
Part of these notes was written as the author's 2013 master thesis. For proper flat schemes over a complete discrete valuation ring of mixed characteristic, we construct an isomorphism of certain subgroups of the Picard group and the first cohomology group of the structure sheaf. When the Picard scheme is available and smooth, it recovers the isomorphism coming from its formal completion. A reinterpretation of an old theorem of Mattuck is given.
Cite
@article{arxiv.1309.6186,
title = {Notes on a p-adic exponential map for the Picard group},
author = {Wataru Kai},
journal= {arXiv preprint arXiv:1309.6186},
year = {2017}
}
Comments
v2: exposition improved. 14 pages