A comparison theorem for l-adic cohomology

1998/06/01 by R. HUBER, R. Huber · 3 citations
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Alkaloids: synthesis and pharmacology

paper · pdf · doi:10.1023/a:1000345530725

Abstract

We show that, for certain types of rigid analytic varieties X and constructible l-adic sheaves (F _n ) _n on, one has H ^p_c (X,(F _n ) _n ) \stackrel∼\longrightarrow lim_\stackrel\scriptstyle\longleftarrow \scriptstylen H ^p_c (X,F _n ). As an application we obtain that, for an algebraic variety X and associated rigid analytic variety X ^rig , the l-adic cohomology of X and X ^rig agree.

Cited by

• Slopes and weights of ℓ-adic cohomology of rigid spaces
• Compactly supported cohomology and nearby cycle cohomology of open Shimura varieties of PEL type
• The generic fiber of moduli spaces of bounded local G-shtukas

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