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#grothendieck's_connectedness_theorem

Grothendieck's connectedness theorem

In mathematics, Grothendieck's connectedness theorem, states that if A is a complete Noetherian 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.

Tue 26th

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Grothendieck's connectedness theorem Connectedness theorem Fulton–Hansen connectedness theorem Zariski's main theorem List of things named after Alexander Grothendieck List of theorems Seifert–Van Kampen theorem Theorem of Bertini Riemann–Roch theorem Brown's representability theorem

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