Abstract
We provide a relative version of the trace map from the work of Beyer, which can be associated to any finite étale morphism X→Y\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ X \\rightarrow Y$$\\end{document} of smooth rigid Stein spaces and which then relates the Serre duality on X with the Serre duality on Y. Furthermore, we consider the behaviour of any rigid Stein space under (completed) base change to any complete extension field and deduce a commutative diagram relating Serre duality over the base field with the Serre duality over the extension field.
Published Version
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