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Grothendieck's connectedness theorem : ウィキペディア英語版 | Grothendieck's connectedness theorem In mathematics, Grothendieck's connectedness theorem (, ) states that if ''A'' is a complete local ring whose spectrum is ''k''-connected and ''f'' is in the maximal ideal, then Spec(''A''/''fA'') is (''k'' − 1)-connected. Here a Noetherian scheme is called ''k''-connected if its dimension is greater than ''k'' and the complement of every closed subset of dimension less than ''k'' is connected. Grothendieck XIII.2.1 It is a local analogue of Bertini's theorem. ==References==
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