Etale cohomology of algebraizable rigid analytic varieties via nearby cycles over general bases

Abstract: One of the most fundamental results in the study of étale cohomology of rigid analytic varieties is the comparison with the nearby cycle cohomology, which gives a canonical isomorphism between the cohomology of an algebraizable rigid analytic variety and the cohomology of the nearby cycle. I will discuss a generalization of this comparison result to the relative case: For an algebraizable morphism, the compactly supported higher direct image sheaves are identified, up to replacing the target by a blowup, with a generalization of the nearby cycle cohomology, which is given by the theory of nearby cycles over general bases. This result can be used to show the existence of a tubular neighborhood that doesn’t change the cohomology for algebraizable families.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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