Integral $p$-adic cohomology theories
Tomoyuki Abe, Richard Crew
TL;DR
This paper proves that there are no finitely generated integral $p$-adic cohomology theories satisfying certain descent properties and matching rigid cohomology rationally.
Contribution
It establishes the non-existence of a specific class of integral $p$-adic cohomology theories with desired properties.
Findings
No finitely generated integral $p$-adic cohomology satisfying finite étale descent exists.
Such cohomology theories cannot have rational cohomology coinciding with rigid cohomology.
The result constrains possible approaches to $p$-adic cohomology theories.
Abstract
In this paper, we show the non-existence of finitely generated integral -adic cohomology which satisfies finite \'etale descent and the associated rational cohomology coincides with rigid cohomology.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Advanced Combinatorial Mathematics