Related papers: Q-points in the Tukey order
Let f(z) be a rational function of degree at least 2 with coefficients in a number field K, and assume that the second iterate f^2(z) of f(z) is not a polynomial. The second author previously proved that for any b in K, the forward orbit…
Q-balls are non-topological solitons in a large family of field theories. We focus on the existence of $U(1)$ gauged Q-balls for a field theory with sixth-order potential. The problem can be reduced to proving the existence of critical…
We continue the study of the pseudo-intersection property with respect to an ideal introduced in \cite{TomNatasha2}. Our theory applies to the study of the Tukey types of general sums of ultrafilters, which, as evidenced by the results of…
All possible products of all elements of an odd order finite group are considered. A set of all such products is called as a K-set. A hypothesis of K-set coincidence of any group of an odd order with its commutant is proposed and the…
It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra…
This paper investigates conditions under which canonical cofinal maps of the following three types exist: continuous, generated by finitary end-extension preserving maps, and generated by finitary maps. The main theorems prove that every…
In this paper we have studied some important topological properties and characterization of I^K-convergence of functions which is a common generalization of I*-convergence of functions. We also introduce the idea of I^K*-convergence and…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
If, for a subset S of Z^k, we compare the conditions of being parametrizable (a) by a single k-tuple of polynomials with integer coefficients, (b) by a single k-tuple of integer-valued polynomials and, (c) by finitely many k-tuples of…
We show that pointlike sets are decidable for the pseudovariety of finite semigroups whose idempotent-generated subsemigroup is R-trivial. Notably, our proof is constructive: we provide an explicit relational morphism which computes the…
We prove several results on the number of rational points on open subsets of Kummer varieties of arbitrary dimension. Some of our results are unconditional, and others depend on the Parity Conjecture (a corollary of the Conjecture of Birch…
We present a new property of the trigonometric system arranged in a natural order. It is shown that the sequence of subspaces of trigonometric polynomials is optimal in the sense of order of convergence on convolution classes K*Up in Lq for…
We consider various problems related to finding points in $\Q^{2}$ and in $\Q^{3}$ which lie at rational distance from the vertices of some specified geometric object, for example, a square or rectangle in $\Q^{2}$, and a cube or…
There are many families of functions on partitions, such as the shifted symmetric functions, for which the corresponding q-brackets are quasimodular forms. We extend these families so that the corresponding q-brackets are quasimodular for a…
We consider in general two-block substitutions and their fixed points. We prove that some of them have a simple structure: their fixed points are morphic sequences. Others are intrinsically more complex, such as the Kolakoski sequence. We…
It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case…
Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.
In this paper, we study some new examples of ideals on $\omega$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order -- known as the…
We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.