5 papers
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…
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…
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…
Rank Selection and Depth Conditions for Balanced Simplicial Complexes
Brent Holmes, Justin Lyle
We prove some new rank selection theorems for balanced simplicial complexes. Specifically, we prove that rank selected subcomplexes of balanced simplicial complexes satisfying Serr…
Hom and Ext, Revisited
Hailong Dao, Mohammad Eghbali, Justin Lyle
Let be a commutative Noetherian local ring and be finitely generated -modules. We prove a number of results of the form: if $\mbox{Hom}_R(M,N)$ has some nice propertie…