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Publications [#243914] of Ezra Miller

Papers Published

  1. Miller, E, The Alexander duality functors and local duality with monomial support, Journal of Algebra, vol. 231 no. 1 (September, 2000), pp. 180-234, Elsevier BV [MR2001k:13028], [pdf], [doi]
    (last updated on 2021/05/08)

    Alexander duality is made into a functor which extends the notion for monomial ideals to any finitely generated N -graded module. The functors associated with Alexander duality provide a duality on the level of free and injective resolutions, and numerous Bass and Betti number relations result as corollaries. A minimal injective resolution of a module M is equivalent to the injective resolution of its Alexander dual and contains all of the maps in the minimal free resolution of M over every Z -graded localization. Results are obtained on the interaction of duality for resolutions with cellular resolutions and lcm-lattices. Using injective resolutions, theorems of Eagon, Reiner, and Terai are generalized to all N -graded modules: the projective dimension of M equals the support-regularity of its Alexander dual, and M is Cohen-Macaulay if and only if its Alexander dual has a support-linear free resolution. Alexander duality is applied in the context of the Z -graded local cohomology functors H (-) for squarefree monomial ideals I in the polynomial ring S, proving a duality directly generalizing local duality, which is the case when I=m is maximal. In the process, a new flat complex for calculating local cohomology at monomial ideals is introduced, showing, as a consequence, that Terai's formula for the Hilbert series of H (S) is equivalent to Hochster's for H (S/I). © 2000 Academic Press. n n n n i i n-i I I m
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