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A comparison theorem for l-adic cohomology

Published online by Cambridge University Press:  04 December 2007

R. HUBER
R. HUBER
Affiliation:
Fachbereich Mathematik, Bergische Universität, Gauβstr. 20, 42097 Wuppertal, Germany. e-mail: huber@math.uni-wuppertal.de
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Abstract

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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$_n$)$_n$) ${\stackrel{\sim}{\longrightarrow}} {\displaystyle\lim_{\stackrel{\scriptstyle{\longleftarrow}} {\scriptstyle{n}}}}$ 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.

Keywords

l-adic cohomologyrigid analytic varietiesalgebraic varieties.
Type
Research Article
Information
Compositio Mathematica , Volume 112 , Issue 2 , June 1998 , pp. 217 - 235
Copyright
© 1998 Kluwer Academic Publishers