In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.

A non-erasing morphism is weakly unambiguous with respect to a pattern if no other non-erasing morphism maps the pattern to the same image. If the size of the target alphabet is at least three, then the patterns for which there exists a length-increasing weakly unambiguous morphism can be characterized using the concept of loyal neighbors of variables. In this article this characterization is g...

Let R be the homogeneous coordinate ring of Grassmannian G=Gr(2,n) defined over an algebraically closed field k characteristic p≥max⁡{n−2,3}. In this paper we give a description decomposition R, considered as graded Rpr-module, for r≥2. This is companion to [16], where case r=1 was treated, and taken together, our results imply that has finite F-representation type (FFRT). Though it expected al...

Let h:X → Y be a finite morphism of smooth connected complete curves over Cp. We show h extends to a finite morphism between semi-stable models of X and Y . 2000 Mathematics Subject Classification: 11G20

Many important systems such as concurrent heap-manipulating programs, communication networks, or distributed algorithms, are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation for the states of these systems, where transitions can be conveniently described by graph transformation rules. We present a framework for the abstraction of graphs sup...