Notes on a \(p\)-adic exponential map for the Picard group

zbMath1423.14054arXiv1309.6186MaRDI QIDQ2328030

Wataru Kai

Publication date: 9 October 2019

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1309.6186

zbMATH Keywords

Picard groupformal groupMattuck's theorem

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Local ground fields in algebraic geometry (14G20) Picard groups (14C22)

Related Items (1)

A note on the exponential map of a real or \(p\)-adic Lie group

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