One of the main goals this paper is to present relation between limit key polynomials and MacLane-Vaquié polynomials. This a continuation work started in [3], where equivalent result for (which are not limit) proved. Moreover, we (Theorem 1.1) that generalizes various results literature.

Abstract Let k be an algebraically closed field, $$l\ne {{\,\textrm{char}\,}}k$$ l ? char k a prime number, and X quasi-projective scheme over . We show that the étale homotopy type of d th symmetric power is $$\tex...

In this article we study the curvature properties of the order complex of a graded poset under a metric that we call the “orthoscheme metric”. In addition to other results, we characterize which rank 4 posets have CAT(0) orthoscheme complexes and by applying this theorem to standard posets and complexes associated with four-generator Artin groups, we are able to show that the 5-string braid gro...

Let K be a field equipped with a discrete valuation v. In a pioneering work, MacLane determined all valuations on K(x) extending v. His work was recently reviewed and generalized by Vaquié, by using the graded algebra of a valuation. We extend Vaquié’s approach by studying residual ideals of the graded algebra as an abstract counterpart of certain residual polynomials which play a key role in t...

In this paper we identify conditions under which the cohomology H∗(ΩMξ; k) for the loop space ΩMξ of the Thom space Mξ of a spherical fibration ξ ↓ B can be a polynomial ring. We use the Eilenberg–Moore spectral sequence which has a particularly simple form when the Euler class e(ξ) ∈ H(B; k) vanishes, or equivalently when an orientation class for the Thom space has trivial square. As a consequ...

We study the finite generation of homotopy groups closed manifolds and CW-complexes by relating it to cohomology their fundamental groups. Our main theorems are as follows: when X X ...

Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman’s theorem states that they precisely specify pseudovarieties, i.e., classes finite algebras closed under products, subalgebras and quotients. In this article, is generalized to Eilenberg-Moore a monad T on category D: we prove class -algebras pseudovariety iff it presentable by profinit...

We prove a strengthened version of a theorem of Lionel Schwartz that says that certain modules over the Steenrod algebra cannot be the mod 2 cohomology of a space. What is most interesting is our method, which replaces his iterated use of the Eilenberg–Moore spectral sequence by a single use of the spectral sequence converging to H(ΩX;Z/2) obtained from the Goodwillie tower for ΣΩX. Much of the...