@article{637ed59bee374e21abef9d54bb4b280c,
title = "Notes on a p-adic exponential map for the picard group",
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.",
keywords = "Formal group, Mattuck's theorem, Picard group",
author = "Wataru Kai",
note = "Funding Information: ACKNOWLEDGMENT. Part of this paper was written as the author{\textquoteright}s 2013 master thesis. During this work, the author was supported by Graduate Program for Leading Graduate Schools, MEXT, Japan. When I started master{\textquoteright}s course in April 2011, there used to be frequent aftershocks of the Tohoku earthquake in Tokyo too. I thank Prof. Shuji Saito for guiding me firmly despite such circumstances. I am also grateful to Prof. Takao Yamazaki for encouragements to polish up this paper for publication. I owe a lot to the referee for numerous suggestions that improved the exposition significantly.",
year = "2019",
doi = "10.3836/tjm/1502179262",
language = "English",
volume = "42",
pages = "35--49",
journal = "Tokyo Journal of Mathematics",
issn = "0387-3870",
publisher = "Publication Committee for the Tokyo Journal of Mathematics",
number = "1",
}