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In algebraic geometry, the ''h'' topology is a Grothendieck topology introduced by Vladimir Voevodsky to study the homology of scheme. It has several variants, such as the ''qfh'' and ''cdh'' topologies. == Definition == Define a morphism of schemes to be ''submersive'' or a ''topological epimorphism'' if it is surjective on points and its codomain has the quotient topology, i.e., a subset of the codomain is open if and only if its preimage is open. A morphism is ''universally submersive'' or a ''universal topological epimorphism'' if it remains a topological epimorphism after any base change.〔SGA I, Exposé IX, définition 2.1〕〔Suslin and Voevodsky, 4.1〕 The covering morphisms of the ''h'' topology are the universal topological epimorphisms. The ''qfh'' topology has the further restriction that its covering morphisms must be quasi-finite. The proper ''cdh'' topology is defined as follows. Let be a proper morphism. Suppose that there exists a closed immersion . If the morphism is an isomorphism, then ''p'' is a covering morphism for the ''cdh'' topology. The ''cd'' stands for ''completely decomposed'' (in the same sense it is used for the Nisnevich topology). An equivalent definition of a covering morphism is that it is a proper morphism ''p'' such that for any point ''x'' of the codomain, the fiber ''p''−1(''x'') contains a point rational over the residue field of ''x''. The ''cdh'' topology is the smallest Grothendieck topology whose covering morphisms include those of the proper ''cdh'' topology and those of the Nisnevich topology. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「H topology」の詳細全文を読む スポンサード リンク
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