相关论文: Nilpotency in the homotopy of simplicial commutati…

In this paper, we study the Andr\'e-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…

We propose a generalization of a conjecture of D. Quillen, on the vanishing of Andr\'e-Quillen homology, to simplicial commutative rings. This conjecture characterizes a notion of local complete intersection, extended to the simplicial…

The use of homological and homotopical devices, such as Tor and Andr\'e-Quillen homology, have found substantial use in characterizing commutative algebras. The primary category setting has been differentially graded algebras and modules,…

In this paper, a strategy is developed studying a simplicial commutative algebra A whose zeroth homotopy group is a Noetherian ring B and whose higher homotopy groups are finite over B. The strategy replaces A with a connected simplicial…

L. Avramov, following D. Quillen, posed a conjecture to the effect that if $R \to A$ is a homomorphism of Noetherian rings then the Andr\'e-Quillen homology on the category of A-modules satisfies: $D_{s}(A|R;-) = 0$ for $s\gg 0$ implies…

We develop a simple theory of Andr\'e-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences…

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…

We adopt the viewpoint that topological And\'e-Quillen theory for commutative $S$-algebras should provide usable (co)homology theories for doing calculations in the sense traditional within Algebraic Topology. Our main emphasis is on…

This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.

This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.

We show that any closed model category of simplicial algebras over an algebraic theory is Quillen equivalent to a proper closed model category. By ``simplicial algebra'' we mean any category of algebras over a simplicial algebraic theory,…

We obtain Andr\'e-Quillen homology for commutative algebras using relative homological algebra in the category of functors on finite pointed sets

The semigroup of the homotopy classes of the self-homotopy maps of a finite complex which induce the trivial homomorphism on homotopy groups is nilpotent. We determine the nilpotency of these semigroups of compact Lie groups and finite Hopf…

We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a…

By careful analysis of the comparison map from a simplicial set to its image under Kan's ex-infinity functor we obtain a new and combinatorial proof that it is a weak homotopy equivalence. Moreover, we obtain a presentation of it as a…

Supernilpotence is a generalization of nilpotence using a recently developed theory of higher-arity commutators for universal algebras. Many important structural properties have been shown to be associated with supernilpotence, and the…

We classify the homotopy types of reduced 2-nilpotent simplicial groups in terms of the homology an d boundary invariants $b,\beta$. This contains as special cases results of J.H.C. Whitehead on 1-connected 4-dimensional complexes and of…

I show that simple finite vertex algebras are commutative, and that the Lie conformal algebra structure underlying a reduced (i.e., without nilpotent elements) finite vertex algebra is nilpotent.

Let A be an associative algebra of arbitrary dimension over a field F and G a finite soluble group of automorphisms of A oforder n, prime to the characteristic of F. We prove that if the fixed-point subalgebra of A under the action of G…

This paper starts by showing that for algebras in a certain class the concepts of weak nilpotency and nilpotency coincide. It goes on to describe some solvability and nilpotency properties of bicommutative algebras, of assosymmetric and of…