Related papers: Canonical extensions via fitted sublocales

Let $K$ be any finite extension of $Q_{p}$, $L$ any finite Galois extension of $K$ and $E$ any finite large enough coefficient field containing $L$. We classify two-dimensional, F-semistable $E$-representations of $G_{K}$, by listing the…

In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of these objects by using the general framework of abstract pattern…

We use Shelah's theory of possible cofinalities in order to solve a problem about ultrafilters. THEOREM. Suppose that $ \lambda $ is a singular cardinal, $ \lambda ' < \lambda $, and the ultrafilter $D$ is $ \kappa $-decomposable for all…

English : In this article we associate to $G$, a truncated $p$-divisible $\mathcal O$-module of given signature, where $\mathcal O$ is a finite unramified extension of $\mathbb{Z}_p$, a filtration of $G$ by sub-$\mathcal O$-modules under…

The duality of finitary biframes as pointfree bitopological spaces is explored. In particular, for a finitary biframe $\mathcal{L}$ the ordered collection of all its pointfree bisubspaces (i.e. its biquotients) is studied. It is shown that…

This thesis establishes a generalised setting with which to unify the study of finite local complexity (FLC) patterns. The abstract notion of a "pattern" is introduced, which may be seen as an analogue of the space group of isometries…

For a non-compact metrizable space $X$, let ${\mathcal E}(X)$ be the set of all one-point metrizable extensions of $X$, and when $X$ is locally compact, let ${\mathcal E}_K(X)$ denote the set of all locally compact elements of ${\mathcal…

Let $\mathcal{E}$ be the $\sigma$-ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\mathcal{E}$, their associated cardinal characteristics (i.e.\…

With a frame $L$ as the truth value table, we study the topological representations for frame-valued domains. We introduce the notions of locally super-compact $L$-topological space and strong locally super-compact $L$-topological space.…

In S. 1 we deal with amalgamation bases, e.g., we define when an a.e.c. $k$ has $(\lambda,\kappa)$-amalgamation which means "many" M in $K^k_\lambda$ are amalgamation bases. We then consider what happens for the class of lf groups. In S. 2…

For a flat $p$-adic formal family $S$ of log points over a complete discrete valuation ring with perfect residue field of mixed characteristics $(0,p)$ and for a simple normal crossing log scheme $X$ over an exact closed log subscheme of…

Grothendieck develops the theory of pro-objects over a category $\mathsf{C}$. The fundamental property of the category $\mathsf{Pro}(\mathsf{C})$ is that there is an embedding $\mathsf{C} \overset{c}{\longrightarrow}…

Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup…

We prove that the derived direct image of the constant sheaf with field coefficients under any proper map with smooth source contains a canonical summand. This summand, which we call the geometric extension, only depends on the generic…

We introduce a generalization of stationary set reflection which we call "filter reflection", and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We prove the independence of filter reflection…

We construct $p$-adic $L$-functions associated with $p$-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in $p$-adic families, and does…

A set X which is a subset of the Cantor set has property (s) (Marczewski (Spzilrajn)) iff for every perfect set P there exists a perfect set Q contained in P such that Q is a subset of X or Q is disjoint from X. Suppose U is a nonprincipal…

We establish the following model-theoretic characterization: profinite $L$-structures, the cofiltered limits of finite $L$-structures,are retracts of ultraproducts of finite $L$-structures. As a consequence, any elementary class of…

We prove that for every singular cardinal mu of cofinality omega, the complete Boolean algebra compP_mu(mu) contains as a complete subalgebra an isomorphic copy of the collapse algebra Comp Col(omega_1,mu^{aleph_0}). Consequently, adding a…

We identify two categories of locally compact objects on an exact category A. They correspond to the well-known constructions of the Beilinson category lim A and the Kato category k(A). We study their mutual relations and compare the two…