Tiberiu Dumitrescu, Cristodor Ionescu
We compute the first Andre-Quillen homology modules for the simple over-rings of integrally closed domains and study an ideal theoretic condition arising from the vanishing of the first homology module.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We prove that the Andre-Quillen homology and cohomology modules of F-finite Z(p)-algebras are finitely generated.
We study the relation between the vanishing of André-Quillen homology and complete intersection flat dimension and we extend some of the existing results in the literature.
André-Quillen homology and ascent of complete intersection flat dimensions
本文利用André-Quillen同调，证明了多种完全相交平坦维数沿具有完全相交闭纤维的本性有限型平坦局部同态的上升定理，并将前人关于满射局部同态维数的结果推广至本性有限型情形。
A Ghost Lemma for Commutative Ring Homomorphisms via André-Quillen Homology
本文利用André-Quillen同调将导出范畴中的幽灵映射理论推广到交换环，证明了环的幽灵引理，并由此得到Kunz定理的特征无关推广及完全交环的类似结果。
We obtain André-Quillen homology for commutative algebras using relative homological algebra in the category of functors on finite pointed sets
These notes are an introduction to basic properties of Andre-Quillen homology for commutative algebras. They are an expanded version of my lectures at the summer school: Interactions between homotopy theory and algebra, University of Chicago, 26th July - 6th August, 2004. The aim is to give fairly complete proofs of characterizations of smooth homomorphisms and of locally complete intersection homomorphisms in terms of vanishing of Andre-Quillen homology. The choice of the material, and the point of view, are guided by these goals.
We compute the Andre-Quillen cohomology of an affine toric variety. The best results are obtained either in the general case for the first three cohomology groups, or in the case of isolated singularities for all cohomology groups, respectively.
Given a homomorphism of commutative noetherian rings $ϕ: R \to S$, Daniel Quillen conjectured in 1970 that if the Andre-Quillen homology functors $D_n(S|R,-)$ vanish for all $n \gg 0$, then they vanish for all $n \ge 3$. We prove the conjecture under the additional hypothesis that there exists a homomorphism of rings $ψ: S \to R$ such that $ϕ\circψ=\id_S$. More precisely, in this case we show that $ψ$ is complete intersection at $ϕ^{-1}(\fn)$ for every prime ideal $\fn$ of $S$. Using these results, we describe all algebra retracts $S\to R\to S$ for which the $S$-algebra $Tor^R(S,S)$ is finitel…
The use of homological and homotopical devices, such as Tor and André-Quillen homology, have found substantial use in characterizing commutative algebras. The primary category setting has been differentially graded algebras and modules, but recently simplicial categories have also proved to be useful settings. In this paper, we take this point of view up a notch by extending some recent uses of homological algebra in characterizing Noetherian commutative algebras to characterizing simplicial commutative algebras having finite Noetherian homotopy through the use of simplicial homotopy theory. T…
L. Avramov, following D. Quillen, posed a conjecture to the effect that if $R \to A$ is a homomorphism of Noetherian rings then the André-Quillen homology on the category of A-modules satisfies: $D_{s}(A|R;-) = 0$ for $s\gg 0$ implies $D_{s}(A|R;-) = 0$ for s>2. In an earlier paper, the author posed an extended version of this conjecture which considered A to be a simplicial commutative R-algebra with Noetherian homotopy such that the characteristic of $π_{0}A$ is non-zero. In addition, a homotopy characterization of such algebras was described. The main goal of this paper is to develop a stra…
In this paper, we study the André-Quillen homology of simplicial commutative $\ell$-algebras, $\ell$ a field, having certain vanishing properties. When $\ell$ has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational case and, as an application, indicate how the algebraic Serre theorem can be used to resolve a conjecture of D. Quillen for algebras of finite type over Noetherian rings, which have non-zero characteristic.
The André-Quillen cohomology of commutative monoids
本文指出交换幺半群的 Beck 模块等价于相关分次交换环上的模，证明其 Quillen 同调是 André-Quillen 同调的特例，并发展分次形式化理论验证了 Grillet 部分上链复形与 Barr 修正的 Harrison 上链复形的联系。
Quillen's Fundamental Spectral Sequences Revisited
本文针对 Quillen 基本谱序列证明缺失或不完整的问题，系统梳理相关微妙结构，给出可读、严谨且详尽的完整证明。
We propose a generalization of a conjecture of D. Quillen, on the vanishing of André-Quillen homology, to simplicial commutative rings. This conjecture characterizes a notion of local complete intersection, extended to the simplicial setting, under a suitable hypothesis on the local characteristic. Further, under the condition of finite-type homology, we then prove the conjecture in the case of a simplicial commutative algebra augmented over a field of non-zero characteristic. As a consequence, we obtain a proof of Quillen's conjecture for a Noetherian commutative algebra - again augmented ove…
André-Quillen homology of Rees algebras and extended Rees algebras
本文研究Rees代数与扩张Rees代数的André-Quillen同调，证明了Proj R(I)为完全交的等价条件，给出扩张Rees代数的对应结论，并计算了Cohen-Macaulay整环情形下H₁(J)的秩与自由轨迹。
We show that a modification of the proof of a result of Gulliksen gives an elementary proof of the following important theorem by Avramov: if $(A,k) \to (B,l)$ is a homomorphism of noetherian local rings and $B$ is of finite flat dimension over $A$, then the homomorphism induced in André-Quillen homology modules $H_2(A,l,l)\to H_2(B,l,l)$ is injective.
In this paper, we study simplicial commutative algebras with finite André-Quillen homology. Here we restrict our focus to simplicial algebras having characteristic 2. Our aim is to find a generalization of results established by the author. Our goal is to replace the finiteness condition on homotopy with a weaker condition expressed in terms of nilpotency for the action of the homotopy operations. Coupled with the finiteness assumption on André-Quillen homology, this nilpotency condition provides a way to bound the height at which the homology vanishes. As a consequence, we establish a special…
Classical definitions of locally complete intersection (l.c.i.) homomorphisms of commutative rings are limited to maps that are essentially of finite type, or flat. The concept introduced in this paper is meaningful for homomorphisms phi : R \longrightarrow S of commutative noetherian rings. It is defined in terms of the structure of phi in a formal neighborhood of each point of Spec S. We characterize the l.c.i. property by different conditions on the vanishing of the André-Quillen homology of the R-algebra S. One of these descriptions establishes a very general form of a conjecture of Quille…
Relying on the computation of the Andre-Quillen homology groups for unstable Hopf algebras, we prove that the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra.
A quasi-complete intersection (q.c.i.) ideal of a local ring is an ideal with "free exterior Koszul homology"; the definition can also be understood in terms of vanishing of André-Quillen homology functors. Principal q.c.i. ideals are well understood, but few constructions are known to produce q.c.i. ideals of grade zero that are not principal. This paper examines the structure of q.c.i. ideals. We exhibit conditions on a ring $R$ which guarantee that every q.c.i. ideal of $R$ is principal. On the other hand, we give an example of a minimal q.c.i. deal $I$ which does not contain any principal …
For a commutative ring R with an ideal I, generated by a finite regular sequence, we construct differential graded algebras which provide R-free resolutions of I^s and of R/I^s for s>0 and which generalise the Koszul resolution. We derive these from a certain multiplicative double complex. By means of a Cartan-Eilenberg spectral sequence we express Tor_*^R(R/I,R/I^s) and Tor_*^R(R/I, I^s) in terms of exact sequences and find that they are free as R/I-modules. Except for R/I, their product structure turns out to be trivial; instead, we consider an exterior product. The paper is based on ideas b…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。