Display structures on de Rham-Witt cohomology

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 E₁ 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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Bielefeld

Year

2022

Author dc:creator

• Schrödter, Karsten

Repository record source_url

https://pub.uni-bielefeld.de/record/2968135

OAI identifier oai:identifier

oai:pub.uni-bielefeld.de:2968135