Zobrazeno 1 - 10
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pro vyhledávání: '"Faridian, A."'
Autor:
Faridian, Hossein
Quillen's fundamental spectral sequences relate Andr\'{e}-Quillen homology and cohomology to Tor and Ext functors. The five-term exact sequences arising from these spectral sequences are leveraged to characterize regular and complete intersection loc
Externí odkaz:
http://arxiv.org/abs/2405.04709
Autor:
Faridian, Hossein
This expository article sets forth a self-contained and purely algebraic proof of a deep result of Quillen stating that the category of simplicial commutative algebras over a commutative ring is a model category. This is accomplished by starting from
Externí odkaz:
http://arxiv.org/abs/2405.01752
Autor:
Faridian, Hossein
We prove that if $f:R \rightarrow S$ is a local homomorphism of noetherian local rings of finite flat dimension and $M$ is a non-zero finitely generated $S$-module whose Gorenstein flat dimension over $R$ is bounded by the difference of the embedding
Externí odkaz:
http://arxiv.org/abs/2402.06834
Autor:
Faridian, Hossein
We prove that if $f:R \rightarrow S$ is a local homomorphism of noetherian local rings, and $M$ is a non-zero finitely generated or artinian $S$-module whose injective dimension over $R$ is bounded by the difference of the embedding dimensions of $R$
Externí odkaz:
http://arxiv.org/abs/2307.13121
Autor:
Faridian, Hossein
This expository note delves into the theory of projective modules parallel to the one developed for injective modules by Matlis. Given a perfect ring $R$, we present a characterization of indecomposable projective $R$-modules and describe a one-to-on
Externí odkaz:
http://arxiv.org/abs/2011.08086
Autor:
Faridian, Hossein
This thesis is comprised of three chapters. The first chapter deals with bounded complexes of Gorenstein projective and Gorenstein injective modules. Deploying methods of relative homological algebra, we approximate such complexes with bounded comple
Externí odkaz:
http://arxiv.org/abs/2010.03013
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Let $R$ be a commutative noetherian ring, and $\mathcal{Z}$ a stable under specialization subset of $\Spec(R)$. We introduce a notion of $\mathcal{Z}$-cofiniteness and study its main properties. In the case $\dim(\mathcal{Z})\leq 1$, or $\dim(R)\leq
Externí odkaz:
http://arxiv.org/abs/1711.05534
Autor:
Faridian, Hossein
This expository article delves into the Greenlees-May Duality Theorem which is widely thought of as a far-reaching generalization of the Grothendieck's Local Duality Theorem. This theorem is not addressed in the literature as it merits and its proof
Externí odkaz:
http://arxiv.org/abs/1706.06072