Geometric invariant theory (GIT) was developed in the 1960s by Mumford in order to construct quotients of reductive group actions on algebraic varieties and hence to construct and study a number of moduli spaces, including, for example, moduli spaces of bundles over a nonsingular projective curve [26, 28]. Moduli spaces often arise naturally as quotients of varieties by algebraic group actions,...

The theory of exact C∗-algebras was introduced by Kirchberg and has been influential in recent development of C∗-algebras. A fundamental result on exact C∗-algebras is a local characterization of exactness. The notion of weakly exact von Neumann algebras was also introduced by Kirchberg. In this paper, we give a local characterization of weak exactness. As a corollary, we prove that a discrete ...

This paper surveys a few applications of algebro-geometric moduli theory to issues concerning the distribution of rational points in algebraic varieties. A few well known arithmetic problems with their expected answers (the socalled “diophantine conjectures”) are introduced in section 2, explaining their connection with a circle of ideas, whose goal is to find a unifying theme in analytic, diff...

Given an 80-adjacency doxel-based digital four-dimensional hypervolume V , we construct here an associated oriented 4–dimensional polytopal cell complex K(V ), having the same integer homological information (that related to n-dimensional holes that object has) than V . This is the first step toward the construction of an algebraic-topological representation (AT-model) for V , which suitably co...

Logics as Dialgebras Alessandra Palmigiano Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona Abstract The aim of this report is to propose a line of research that studies the connections between the theory of consequence operators as developed in [1] and [4] and the theory of dialgebras. The first steps in this direction are taken in this report, namely some of...

In this note we characterize, in algebraic and geometric terms, when a graded vanishing ideal is generated by binomials over any field K. 2010 MSC: 13F20, 13C05, 14H45

As we observed in [3], one can also interpret the sums S(α;β) as special cases of the correlation sums arising in our work on algebraic twists of modular forms, and we also noted that our more general results and techniques had, as special case, this theorem of Birch and Bombieri. Very recently, Y. Zhang [12, Lemma 12] made a crucial use of this estimate in his work on bounded gaps between prim...

This expository paper discusses a few of the results concerning the structure theory and representation theory of algebraic groups over a fixed algebraically closed field K, such as the linearization of affine groups, the Jordan-Chevalley decomposition, and the Lie-Kolchin theorem.

Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G-complete reducibility under separable field extensions. Part of our proof relies on the recently established Tits Centre Conjecture for the spherical building of the reductive group G.

We present an algebraic construction of the coboundary of a given cycle as a simpler alternative to the geometric one introduced in [4, 5].