Compositio Mathematica

A comparison theorem for l-adic cohomology

a1 Fachbereich Mathematik, Bergische Universität, Gau[beta]str. 20, 42097 Wuppertal, Germany. e-mail: [email protected]

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huber r   [Google Scholar] 


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.

Key Words: l-adic cohomology; rigid analytic varieties; algebraic varieties..