A complex affine Poisson algebra is said to satisfy the Dixmier-Moeglin equivalence if cores of maximal ideals are precisely those prime that locally closed in spectrum P.spec and if, moreover, these whose extended centers exactly numbers. In this paper, we provide some topological criteria for terms poset (P.spec A, ⊆) symplectic leaf or core stratification on its spectrum. particular, prove Z...

is an isomorphism. Here F : X −→ X denotes the Frobenius morphism on X and H denotes the a cohomology sheaf of F∗Ω•X . If the variety is not smooth, not much is known about the properties of the Cartier operator and the poor behaviour of the deRham complex in this case makes its study difficult. If one substitutes the deRham complex with the Zariski-deRham complex the situation is better. For e...

This paper clarifies some aspects of Lorentzian topology change, and it extends to a wider class of spacetimes previous results of Geroch and Tipler that show that topology change is only to be had at a price. The scenarios studied here are ones in which an initial spacelike surface is joined by a connected “interpolating spacetime” to a final spacelike surface, possibly of different topology. ...

It is known that any factorization of a local birational morphism f: Spec 5 —» SpecJ? of nonsingular (affine) schemes of arbitrary dimension via other nonsingular schemes must be finite in length. This fact generalizes the classical Local Factorization Theorem of Zariski and Abhyankar, which states that there is a unique such factorization, that given by quadratic transformations, in the surfac...

Employing the notions of the strong $L$-topology introduced by Zhangand the $L$-frame introduced by Yao  and the concept of $L$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf St$L$-Top} of strong$L$-topological spaces, {bf S$L$-Loc} of strict $L$-locales and{bf $L$-EnTopSys} of $L$-enriched topological systems. All of theseconcepts are ...

We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a (virtual) simple factor. In particular for rank one or simple Lie groups, Zariski dense subgroups with non-empty domain of discontinuity have discrete commensurato...

The book contains a collection of articles by participants of the Working Week on Resolution of Singularities held at Obergurgl in Tirol, September 7-14, 1997. It is dedicated to Oscar Zariski, the founder of the school of algebraic geometry in the United States. During his long career as a mathematician he obtained ground-breaking results in algebra and algebraic geometry. Many years of his ca...

1.1. Sites. We begin with the underlying idea for a Grothendieck topology. Consider your favorite topological space X. Its topology, don’t use the Zariski topology, is determined by the partially ordered category UX consisting of all the open subsets of X ordered with respect to inclusion. In order to verify that a presheaf is a sheaf on X, we must first construct all possible coverings U = (Ui...

— In this paper we show how to recover a special class of valuations (which generalize in a natural way the Zariski prime divisors) of function fields from the Galois theory of the functions fields in discussion. These valuations play a central role in the birational anabelian geometry and related questions. Résumé (Théorie de Galois pro-` des diviseurs premiers de Zariski) Dans cet article nou...