{"id":{"repo_id":"bielefeld","oai_identifier":"oai:pub.uni-bielefeld.de:2968135"},"canonical_url":"https://search.dev.ndltd.org/etd/bielefeld/oai:pub.uni-bielefeld.de:2968135","repository":{"repo_id":"bielefeld","name":"Universität Bielefeld","base_url":"https://pub.uni-bielefeld.de/oai"},"display":{"title":"Display structures on de Rham-Witt cohomology","abstract":"Let $p$ be a prime number and $R$ be a noetherian and $F$-finite ring where $p \\in R$ is nilpotent. In this thesis we prove that the crystalline cohomology of a smooth and proper scheme $X$ over $R$ carries a display structure $\\underline{P}^l$ if the crystalline cohomology $H^l_{crys}(X,W(R))$ is a finite projective $W(R)$-module, the de Rham spectral sequence degenerates at $E_1$ and the cohomologies $H^b(X,\\Omega_{X/R}^a)$ are finite projective $R$-modules for all $a,b \\ge 0$. This was conjectured by Langer and Zink [LZD]. We use the formalism of predisplays from [La18], more precisely we show that $\\underline{P}^l$ is a display over the Witt-frame $\\underline{W}(R)$. This is achieved by constructing and investigating a complex $\\underline{W}\\Omega_{X/R}^{\\bullet}$ of graded $\\underline{W}R$-modules on $X$ admitting extra structure whose hypercohomology equals $\\underline{P}^l$.","abstract_html":"Let $p$ be a prime number and $R$ be a noetherian and $F$-finite ring where $p \\in R$ is nilpotent. In this thesis we prove that the crystalline cohomology of a smooth and proper scheme $X$ over $R$ carries a display structure <span class=\"etd-inline-math\">\\underline{P}<sup>l</sup></span> if the crystalline cohomology <span class=\"etd-inline-math\">H<sup>l</sup><sub>crys</sub>(X,W(R))</span> is a finite projective $W(R)$-module, the de Rham spectral sequence degenerates at <span class=\"etd-inline-math\">E<sub>1</sub></span> and the cohomologies <span class=\"etd-inline-math\">H<sup>b</sup>(X,\\Omega<sub>X/R</sub><sup>a</sup>)</span> are finite projective $R$-modules for all $a,b \\ge 0$. This was conjectured by Langer and Zink [LZD]. We use the formalism of predisplays from [La18], more precisely we show that <span class=\"etd-inline-math\">\\underline{P}<sup>l</sup></span> is a display over the Witt-frame $\\underline{W}(R)$. This is achieved by constructing and investigating a complex <span class=\"etd-inline-math\">\\underline{W}\\Omega<sub>X/R</sub><sup>\\bullet</sup></span> of graded $\\underline{W}R$-modules on $X$ admitting extra structure whose hypercohomology equals <span class=\"etd-inline-math\">\\underline{P}<sup>l</sup></span>.","abstract_has_math":true,"creators":["Schrödter, Karsten"],"institution":"Universität Bielefeld","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-12-21","date_published":"2022-12-21","updated_at":"2026-07-27T18:50:04Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://pub.uni-bielefeld.de/record/2968135","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Schrödter, Karsten"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universitätsbibliothek Bielefeld"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Bielefeld"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let $p$ be a prime number and $R$ be a noetherian and $F$-finite ring where $p \\in R$ is nilpotent. In this thesis we prove that the crystalline cohomology of a smooth and proper scheme $X$ over $R$ carries a display structure $\\underline{P}^l$ if the crystalline cohomology $H^l_{crys}(X,W(R))$ is a finite projective $W(R)$-module, the de Rham spectral sequence degenerates at $E_1$ and the cohomologies $H^b(X,\\Omega_{X/R}^a)$ are finite projective $R$-modules for all $a,b \\ge 0$. This was conjectured by Langer and Zink [LZD]. We use the formalism of predisplays from [La18], more precisely we show that $\\underline{P}^l$ is a display over the Witt-frame $\\underline{W}(R)$. This is achieved by constructing and investigating a complex $\\underline{W}\\Omega_{X/R}^{\\bullet}$ of graded $\\underline{W}R$-modules on $X$ admitting extra structure whose hypercohomology equals $\\underline{P}^l$."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Display structures on de Rham-Witt cohomology"]}]}],"canonical_facts":{"dc:creator":["Schrödter, Karsten"],"dc:description.abstract":["Let $p$ be a prime number and $R$ be a noetherian and $F$-finite ring where $p \\in R$ is nilpotent. In this thesis we prove that the crystalline cohomology of a smooth and proper scheme $X$ over $R$ carries a display structure $\\underline{P}^l$ if the crystalline cohomology $H^l_{crys}(X,W(R))$ is a finite projective $W(R)$-module, the de Rham spectral sequence degenerates at $E_1$ and the cohomologies $H^b(X,\\Omega_{X/R}^a)$ are finite projective $R$-modules for all $a,b \\ge 0$. This was conjectured by Langer and Zink [LZD]. We use the formalism of predisplays from [La18], more precisely we show that $\\underline{P}^l$ is a display over the Witt-frame $\\underline{W}(R)$. This is achieved by constructing and investigating a complex $\\underline{W}\\Omega_{X/R}^{\\bullet}$ of graded $\\underline{W}R$-modules on $X$ admitting extra structure whose hypercohomology equals $\\underline{P}^l$."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universitätsbibliothek Bielefeld"],"dc:title":["Display structures on de Rham-Witt cohomology"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Bielefeld"]},"updated_at":"2026-07-27T18:50:04Z"}