Notes on a p-adic exponential map for the picard group

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For proper flat schemes over complete discrete valuation rings 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 functor is representable and smooth, our construction recovers and gives finer information to the isomorphism coming from its formal completion. An alternative proof of an old theorem of Mattuck is given.

Original languageEnglish
Pages (from-to)35-49
Number of pages15
JournalTokyo Journal of Mathematics
Issue number1
Publication statusPublished - 2019


  • Formal group
  • Mattuck's theorem
  • Picard group

ASJC Scopus subject areas

  • Mathematics(all)


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