Topological Representation of Sheaf Cohomology of Sites |
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Authors: | Carsten Butz Ieke Moerdijk |
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Institution: | (1) Mathematisch Instituut, Universiteit Utrecht, Postbus 80.010, NL-3508 TA Utrecht, The Netherlands e-mail;(2) BRICS, Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus, Denmark |
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Abstract: | For a site & (with enough points), we construct a topological space X(&) and a full embedding * of the category of sheaves on & into those on X
(&) (i.e., a morphism of toposes :Sh (X(&)) Sh(&)). The embedding will be shown to induce a full embedding of derived categories, hence isomorphisms H*(&,A) = H*(X(&), *A) for any Abelian sheaf A on &. As a particular case, this will give for any scheme Y a topological space X
(Y) and a functorial isomorphism between the étale cohomology H*(Y
ét,A) and the ordinary sheaf cohomology H*(X((Y),),*A), for any sheaf A for the étale topology on Y. |
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Keywords: | Sheaf cohomology site é tale cohomology topos with enough points derived category |
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