The Primitive Comparison Theorem in characteristic p

Abstract

We prove an analogue of Scholze’s Primitive Comparison Theorem for proper rigid spaces over an algebraically closed non-archimedean field K of characteristic p. This implies a v-topological version of the Primitive Comparison Theorem for proper finite type morphisms f:X→Y\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f{:}\\,X\\rightarrow Y$$\\end{document} of analytic adic spaces over Zp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}_p$$\\end{document}. We deduce new cases of the Proper Base Change Theorem for p-torsion coefficients and the Künneth formula in this setting.