English

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.

Keywords

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

R2 v1 2026-06-22T01:33:04.783Z