Tokyo Journal of Mathematics

Notes on a $p$-adic Exponential Map for the Picard Group

Wataru KAI

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Abstract

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.

Article information

Source
Tokyo J. Math., Volume 42, Number 1 (2019), 35-49.

Dates
First available in Project Euclid: 18 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1563436912

Mathematical Reviews number (MathSciNet)
MR3982048

Zentralblatt MATH identifier
07114899

Subjects
Primary: 14C22: Picard groups

Citation

KAI, Wataru. Notes on a $p$-adic Exponential Map for the Picard Group. Tokyo J. Math. 42 (2019), no. 1, 35--49. https://projecteuclid.org/euclid.tjm/1563436912


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References

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