DG structure on length 3 trimming complexes and applications to Tor algebras
K VandeBogert - Journal of Pure and Applied Algebra, 2022 - Elsevier
Journal of Pure and Applied Algebra, 2022•Elsevier
In this paper, we consider the iterated trimming complex associated to data yielding a
complex of length 3. We compute an explicit algebra structure in this complex in terms of the
algebra structures of the associated input data. Moreover, it is shown that many of these
products become trivial after descending to homology. We apply these results to the problem
of realizability for Tor-algebras of grade 3 perfect ideals, and show that under mild
hypotheses, the process of “trimming” an ideal preserves Tor-algebra class. In particular, we …
complex of length 3. We compute an explicit algebra structure in this complex in terms of the
algebra structures of the associated input data. Moreover, it is shown that many of these
products become trivial after descending to homology. We apply these results to the problem
of realizability for Tor-algebras of grade 3 perfect ideals, and show that under mild
hypotheses, the process of “trimming” an ideal preserves Tor-algebra class. In particular, we …
In this paper, we consider the iterated trimming complex associated to data yielding a complex of length 3. We compute an explicit algebra structure in this complex in terms of the algebra structures of the associated input data. Moreover, it is shown that many of these products become trivial after descending to homology. We apply these results to the problem of realizability for Tor-algebras of grade 3 perfect ideals, and show that under mild hypotheses, the process of “trimming” an ideal preserves Tor-algebra class. In particular, we construct new classes of ideals in arbitrary regular local rings defining rings realizing Tor-algebra classes G (r) and H (p, q) for a prescribed set of homological data.
Elsevier
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