<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "A Relative Trace Map and its Compatibility with Serre Duality in Rigid Analytic Geometry"^^ . "Given a complete non-archimedean valued field K, we discuss a relative trace map\r\nattached to any finite étale morphism of smooth rigid-analytic Stein spaces over K\r\nand prove that it is compatible with the trace maps that arise in the Serre duality\r\ntheory on the respective Stein spaces. Our proof builds on the technique of inves-\r\ntigating the trace map of a rigid Stein space via a relation between algebraic local\r\ncohomology and compactly supported rigid cohomology established in the work of\r\nBeyer [Bey97a]. For this purpose we also prove a generalization of a theorem of\r\nBosch [Bos77] which concerns the connectedness of formal fibers of a distinguished\r\naffinoid space. This closes an argumentative gap in [Bey97a].\r\nFurthermore, we consider the behaviour of any rigid-analytic Stein space and its\r\ntrace map under (completed) base change to any complete extension field K′/K\r\nand prove that there are natural base change comparison maps that yield a com-\r\nmutative diagram relating Serre duality over K with Serre duality over K′.\r\nFinally we discuss the recent work of Abe and Lazda [AL20], which constructs a\r\ntrace map on proper pushforwards of analytic adic spaces, and we explain how some\r\nof their results can be related to ours (via Huber’s functor from the category of rigid\r\nanalytic varieties to the category of adic spaces)."^^ . "2023" . . . . . . . "Milan"^^ . "Malcic"^^ . "Milan Malcic"^^ . . . . . . "A Relative Trace Map and its Compatibility with Serre Duality in Rigid Analytic Geometry (PDF)"^^ . . . "Dissertation Milan Malcic.pdf"^^ . . . "A Relative Trace Map and its Compatibility with Serre Duality in Rigid Analytic Geometry (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "A Relative Trace Map and its Compatibility with Serre Duality in Rigid Analytic Geometry (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "A Relative Trace Map and its Compatibility with Serre Duality in Rigid Analytic Geometry (Other)"^^ . . . . . . "preview.jpg"^^ . . . "A Relative Trace Map and its Compatibility with Serre Duality in Rigid Analytic Geometry (Other)"^^ . . . . . . "medium.jpg"^^ . . . "A Relative Trace Map and its Compatibility with Serre Duality in Rigid Analytic Geometry (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #33617 \n\nA Relative Trace Map and its Compatibility with Serre Duality in Rigid Analytic Geometry\n\n" . "text/html" . . . "510 Mathematik"@de . "510 Mathematics"@en . .