The Independence Theorem for the congruence lattice and the auto-morphism group of a nite lattice was proved by V. A. Baranski and A. Urquhart. Both proofs utilize the characterization theorem of congruence lattices of nite lattices (as nite distributive lattices) and the characterization theorem of auto-morphism groups of nite lattices (as nite groups). In this paper, we introduce a new, stron...

Given a complex space X, we cosidered the problem of finding a hyperbolic model of X. This is an object Ip(X) with a morphism i : X → Ip(X) in such a way that Ip(X) is “hyperbolic” in a suitable sense and i is as close as possible to be an isomorphism. Using the theory of model categories, we found a definition of hyperbolic simplicial sheaf (for the strong topology) that extends the classical ...

We establish a trace formula for rigid varieties X over a complete discretely valued field of equicharacteristic zero, which relates the set of unramified points on X to the Galois action on its étale cohomology. Next, we show that the analytic Milnor fiber of a morphism f at a point x completely determines the analytic germ of f at x. We develop a theory of motivic integration for formal schem...

Let X be the germ of a complex- or real-analytic manifold M at a point x(o) in M, or the henselian germ of an algebraic manifold M over a field k of characteristic zero at a point x(o) in M(k), D subset X a divisor. Under some assumptions on D and its singularities we give a description of the structure, the singularities, and the divisor class group of all finite normal coverings of X ramified...

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

We prove the following. Let R be a Noetherian commutative ring, B a finitely generated R-algebra, and A a pure R-subalgebra of B. Then A is finitely generated over R. In this paper, all rings are commutative. Let A be a ring and B an A-algebra. We say that A → B is pure, or A is a pure subring of B, if for any A-module M , the map M = M ⊗A A → M ⊗A B is injective. Considering the case M = A/I, ...