Comparison between Rigid and Overconvergent Cohomology with Coefficients
Veronika Ertl
TL;DR
This paper introduces overconvergent de Rham-Witt connections for smooth schemes over fields of characteristic p, extending comparison morphisms between different cohomology theories to include coefficients.
Contribution
It generalizes the definition of Bloch and develops overconvergent de Rham-Witt connections, enabling comparison of cohomology theories with coefficients.
Findings
Extended comparison morphisms to include coefficients
Generalized Bloch's definition for overconvergent de Rham-Witt connections
Provided new tools for cohomology theory comparisons
Abstract
For a smooth scheme over a perfect field of characteristic p>0, we generalise a definition of Bloch and introduce overconvergent de Rham-Witt connections. This provides a tool to extend the comparison morphisms of Davis, Langer and Zink between overconvergent de Rham-Witt cohomology and Monsky-Washnitzer respectively rigid cohomology to coefficients.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology