Related papers: Extending maps to profinite completions in finitel…
We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
An extension of the General Coordinate Transformations algebra is constructed by means geometrical consistency conditions. An class of infinite invariants is derived. In particular we construct the consistent extension of the gravitational…
Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we…
We prove the existence of a genus-zero complete maximal map with a prescribed singularity set and an arbitrary number of simple and complete ends. We also discuss the conditions under which this maximal map can be made into a complete…
We construct a notion of derived completion which applies to homomorphisms of commutative S-algebras. We study the relationship of the construction with other constructions of completions, and prove various invariance properties. The…
Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…
We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that $g$-vectors and $E$-invariants of modules are upper…
Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate…
For a finite dimensional vector space equipped with a $\mathbb C$-algebra structure, one can define rational maps using the algebraic structure. In this paper, we describe the growth of the degree sequences for this type of rational maps.
One proves a far-reaching upper bound for the degree of a generically finite rational map between projective varieties over a base field of arbitrary characteristic. The bound is expressed as a product of certain degrees that appear…
We introduce the notion of amenability for affine algebras. We characterize amenability by Folner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
The possibility of extending operations of topological and semitopological algebras to their Stone-\v{C}ech compactification and factorization of continuous functions through homomorphisms to metrizable algebras are investigated. Most…
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
A geometric extension algebra is an extension algebra of a semi-simple perverse sheaf (allowing shifts), e.g. a push-forward of the constant sheaf under a projective map. Particular nice situations arise for collapsings of homogeneous…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
We study the relative Frobenius map associated with a map of derived commutative rings over a field of positive characteristic. As part of this, we examine a relative analog of perfectness and construct a relative inverse limit perfection…
The algebra of exponential fields and their extensions is developed. The focus is on ELA-fields, which are algebraically closed with a surjective exponential map. In this context, finitely presented extensions are defined, it is shown that…
This work investigates the existence of complex structures on 2-step nilpotent Lie algebras arising from finite graphs. We introduce the notion of adapted complex structure, namely a complex structure that maps vertices and edges of the…