0.1. The problem. Roughly speaking, the semistable reduction problem we address here asks for the following: Let X → B be a surjective morphism of complex projective varieties with geometrically integral generic fiber. Find a generically finite proper surjective morphism (that is, an alteration) B1 → B, and a proper birational morphism (that is, a modification) Y → X ×B B1, such that the morphi...

We continue our study on infinitesimal lifting properties of maps between locally noetherian formal schemes started in [3]. In this paper, we focus on some properties which arise specifically in the formal context. In this vein, we make a detailed study of the relationship between the infinitesimal lifting properties of a morphism of formal schemes and those of the corresponding maps of usual s...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a h...

The notion of a state-morphism on pseudoeffect algebras is introduced, and pseudo-effect algebras with distinguished state-morphisms are studied under the name state-morphism pseudo-effect algebras (SMPEAs). It is shown that every SMPEA admits a representation as a (total) state-morphism algebra, and some results from the general theory of state-morphism algebras (that is, algebras endowed with...

1. Brief summary onétale cohomology In this section, k denotes a field, a scheme will mean a separated scheme of finite type over k and a morphism of schemes will mean a morphism over k. We put p = char k. 1.1. Definition and examples ofétale sheaves. A morphism X → Y of schemes is said to bé etale if Ω 1 X/Y = 0 and if X is flat over Y. Example 1.1. An open immersion isétale. The morphism G m ...