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nLab > Latest Changes: Serre's theorem on Proj

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  1.  
    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeJul 31st 2023

    Quick stub, mostly written from memory.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJul 31st 2023

    We prove that an abelian category equipped with an ample sequence of objects is equivalent to the quotient of the category of coherent modules over the corresponding algebra by the subcategory of finite-dimensional modules. In the Noetherian case a similar result was proved by Artin and Zhang.

    diff, v2, current

  3. Minor typo: a \mathcal{O} was missing the backslash in the first sentence.

    Benjamin Ashlock

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 28th 2024

    Added:

    See also

    diff, v5, current

  5. Edit: Serre theorem for quasicoherent sheaves. The kernel of the localization is not just the finite length modules; it is generated by them under all colimits.

    Altan

    diff, v7, current

1 to 5 of 5

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