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math.CO2019
Minimal Cohen-Macaulay Simplicial Complexes
Hailong Dao, Joseph Doolittle, Justin Lyle
We define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give suff…
math.AC2019
Extremal growth of Betti numbers and trivial vanishing of (co)homology
Justin Lyle, Jonathan Montaño
A Cohen-Macaulay local ring satisfies trivial vanishing if for all large implies or has finite projective dimension. If satisfie…
math.AC2019
Maximal Cohen-Macaulay modules that are not locally free on the punctured spectrum
Toshinori Kobayashi, Justin Lyle, Ryo Takahashi
We say that a Cohen-Macaulay local ring has finite -representation type if there exist only finitely many isomorphism classes of indecomposable maxima…