Introduction In a series of earlier papers, ([ST1-4]) we began a systematic study of locally analytic representations of a locally L-analytic group G, where L ⊆ C p is a finite extension of Q p. Such a representation is given by a continuous action of G on a locally convex topological vector space V over a spherically complete extension field K ⊆ C p of L, such that the orbit maps g → gv are lo...

Let X be an Artin stack (always assumed to have quasi-compact and separated diagonal over SpecZ; cf. [2, §1.3]). A coarse moduli space for X is a map π : X → X to an algebraic space such that (i) π is initial among maps from X to algebraic spaces (note that the category of maps from X to an algebraic space is discrete), and (ii) for every algebraically closed field k the map [X (k)]→ X(k) is bi...

We undertake a comprehensive study of measure equivalence between general locally compact, second countable groups, providing operator algebraic and ergodic theoretic reformulations, complete the classification amenable groups within this class up to equivalence.

Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generaliz...

We introduce and discuss a concept of approximation of a topological algebraic system A by finite algebraic systems from a given class K. If A is discrete, this concept agrees with the familiar notion of a local embedding of A in a class K of algebraic systems. One characterization of this concept states that A is locally embedded in K iff it is a subsystem of an ultraproduct of systems from K....

It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the approximations of locally compact groups by more general finite algebraic systems are investigated. It is proved that the approximation of locally compact groups b...

We show that if R is a Jordan Szabó algebraic covariant derivative curvature tensor on a vector space of signature (p, q), where q ≡ 1 mod 2 and p < q or q ≡ 2 mod 4 and p < q − 1, then R = 0. This algebraic result yields an elementary proof of the geometrical fact that any pointwise totally isotropic pseudo-Riemannian manifold with such a signature (p, q) is locally symmetric.