2020/09/29 by Katharina Hübner, Hübner, Katharina
Mathematics · #advanced mathematical theories #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2009.14128
On a smooth discretely ringed adic space X over a field k we define a subsheaf ΩX+ of the sheaf of differentials ΩX. It is defined in a similar way as the subsheaf O+X of OX using Kähler seminorms on ΩX. We give a description of Ω+X in terms of logarithmic differentials. If X is of the form Spa(X,X) for a scheme X and an open subscheme X such that the corresponding log structure on X is smooth, we show that Ω+X(X) is isomorphic to the logarithmic differentials of (X,X).