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  1. Added statement of the fact that any open subset of the underlying topological space of a scheme XX, together with the sheaf of commutative rings on it obtained by restriction of the structure sheaf on XX, defines an open subscheme of XX. Began proof, but not finished yet. Whilst the proof is straightforward, there is something to show; it is not completely trivial.

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorRichard Williamson
    • CommentTimeApr 29th 2018
    • (edited Apr 29th 2018)

    Completed the proof, modulo a couple of basic pieces of commutative algebra. Would be great if someone finds time to write up these (on a different page)! I tried to be a little more careful than seems to be typically the case (compare for example the proof in EGA I (Proposition 2.1.3 in Chapter I) or the stacks project, Lemma 25.9.2), keeping track of the isomorphism between NN and SpecASpec A, and mentioning some points which one needs to convince oneself are true.

    diff, v5, current