Given a set T ⊆ GF(q), |T | = t, wT is defined as the smallest positive integer k for which ∑ y∈T y k 6= 0. It can be shown that wT ≤ t always and wT ≤ t − 1 if the characteristic p divides t. T is called a Vandermonde set if wT ≥ t−1 and a super-Vandermonde set if wT = t. This (extremal) algebraic property is interesting for its own right, but the original motivation comes from finite geometri...

Using the parallel between the preframe and the suplattice approach to locale theory it is shown that the patch construction, as an action on topologies, is the same thing as the process of recovering a discrete poset from its algebraic dcpo (ideal completion).

Using admissibility for a computable model theory for uncountable structures

Expansive algebraic Z-actions corresponding to ideals are characterized by the property that the complex variety of the ideal is disjoint from the multiplicative unit torus. For such actions it is known that the limit for the growth rate of periodic points exists and equals the entropy of the action. We extend this result to actions for which the complex variety intersects the multiplicative to...

We investigate the β-expansion of an algebraic number in an algebraic base β. Using tools from Diophantine approximation, we prove several results that may suggest a strong difference between the asymptotic behaviour of eventually periodic expansions and that of non-eventually periodic expansions.

An algebraic deformation theory of coalgebra morphisms is constructed.

The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group G, G is compact if there exists a measure μ in Soc(L1(G)) such that μ(G) 6= 0. We also prove that G is finite if Soc(M(G)) is closed and every nonzero left ideal in M(G) contains a minima...

This paper surveys some combinatorial aspects of Smith normal form, and more generally, diagonal form. The discussion includes general algebraic properties and interpretations of Smith normal form, critical groups of graphs, and Smith normal form of random integer matrices. We then give some examples of Smith normal form and diagonal form arising from (1) symmetric functions, (2) a result of Ca...

This paper concerns character sheaves of connected reductive algebraic groups defined over non-Archimedean local fields and their relation with characters of smooth representations. Although character sheaves were devised with characters of representations of finite groups of Lie type in mind, character sheaves are perfectly well defined for reductive algebraic groups over any algebraically clo...

Let H be a semisimple algebraic group. We prove the semistable reduction theorem for μ–semistable principal H–bundles over a smooth projective variety X defined over the field C. When X is a smooth projective surface and H is simple, we construct the algebro– geometric Donaldson–Uhlenbeck compactification of the moduli space of μ–semistable principal H–bundles with fixed characteristic classes ...