Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Lyle, Justin"'
Autor:
Lyle, Justin, Maitra, Sarasij
Let $(R,\mathfrak{m})$ be a commutative Noetherian local ring, and suppose $R$ is Cohen-Macaulay with canonical module $\omega_R$. We develop new tools for analyzing questions involving annihilators of several homologically defined objects. Using the
Externí odkaz:
http://arxiv.org/abs/2409.04686
Autor:
Lyle, Justin
Let $R$ be a commutative Noetherian local ring and $M$ a finitely generated $R$-module. We introduce a general form of the classically studied trace map that unifies several notions from the literature. We develop a theory around these objects and us
Externí odkaz:
http://arxiv.org/abs/2311.00220
This paper provides a method to get a noetherian equicharacteristic local UFD with an isolated singularity from a given noetherian complete equicharacteristic local ring, preserving certain properties. This is applied to invesitgate the (non)vanishin
Externí odkaz:
http://arxiv.org/abs/2310.16599
Autor:
Lyle, Justin
Let $R$ be a commutative Noetherian local ring. We study tensor products involving a finitely generated $R$-module $M$ through the natural action of its endomorphism ring. In particular, we study torsion properties of self tensor products in the case
Externí odkaz:
http://arxiv.org/abs/2310.14134
We study a modified version of the classical Ulrich modules, which we call $c$-Ulrich. Unlike the traditional setting, $c$-Ulrich modules always exist. We prove that these modules retain many of the essential properties and applications observed in t
Externí odkaz:
http://arxiv.org/abs/2308.06606
A commutative Noetherian ring $R$ is said to be Tor-persistent if, for any finitely generated $R$-module $M$, the vanishing of $\operatorname{Tor}_i^R(M,M)$ for $i\gg 0$ implies $M$ has finite projective dimension. An open question of Avramov, et. al
Externí odkaz:
http://arxiv.org/abs/2007.09174
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 sufficient conditions for a complex to be minimal Cohen-Macaulay. We show
Externí odkaz:
http://arxiv.org/abs/1905.05043
Autor:
Lyle, Justin, Montaño, Jonathan
A Cohen-Macaulay local ring $R$ satisfies trivial vanishing if $\operatorname{Tor}_i^R(M,N)=0$ for all large $i$ implies $M$ or $N$ has finite projective dimension. If $R$ satisfies trivial vanishing then we also have that $\operatorname{Ext}^i_R(M,N
Externí odkaz:
http://arxiv.org/abs/1903.12324
We say that a Cohen-Macaulay local ring has finite $\operatorname{\mathsf{CM}}_+$-representation type if there exist only finitely many isomorphism classes of indecomposable maximal Cohen-Macaulay modules that are not locally free on the punctured sp
Externí odkaz:
http://arxiv.org/abs/1903.03287
Autor:
Holmes, Brent, Lyle, Justin
We prove some new rank selection theorems for balanced simplicial complexes. Specifically, we prove that rank selected subcomplexes of balanced simplicial complexes satisfying Serre's condition $(S_{\ell})$ retain $(S_{\ell})$. We also provide a form
Externí odkaz:
http://arxiv.org/abs/1802.03129