Related papers: Finite presentability of normal fibre products
We present a sufficient condition for the Riemann hypothesis. This condition is the existence of a special ordering on the set of finite products of distinct odd primes.
We introduce some special presentations on finite groups, that we call "diagonal double Kodaira structures" and whose existence is equivalent to the existence of some special Kodaira fibred surfaces, that we call "diagonal double Kodaira…
Let $\mathcal X$ be a regular variety, flat and proper over a complete regular curve over a finite field, such that the generic fiber $X$ is smooth and geometrically connected. We prove that the Brauer group of $\mathcal X$ is finite if and…
In this paper, we introduce the concept of several products of rough finite state machines. We establish their relationships through coverings and investigate some algebraic properties for these products.
In this note we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if $H$ is a finitely generated normal subgroup of a finitely presented group $G$ with $G/H$ cyclic, then $H$ has…
We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.
We give a finite presentation for the braid twist group of a decorated surface. If the decorated surface arises from a triangulated marked surface without punctures, we obtain a finite presentation for the spherical twist group of the…
A category of FI type is one which is sufficiently similar to finite sets and injections so as to admit nice representation stability results. Several common examples admit a Grothendieck fibration to finite sets and injections. We begin by…
Twin-width is a recently introduced graph parameter with applications in algorithmics, combinatorics, and finite model theory. For graphs of bounded degree, finiteness of twin-width is preserved by quasi-isometry. Thus, through Cayley…
We fix an excellent regular noetherian scheme $S$ over ${\mathbf Z}_{(p)}$ satisfying a certain finiteness condition. For a constructible \'etale sheaf ${\cal F}$ on a regular scheme $X$ of finite type over $S$, we introduce a variant of…
We study weak approximation on rationally connected varieties under an assumption of strong approximation for a "simple" variety or under Schinzel's hypothesis. We also get some unconditional results.
We consider the preservation of properties of being finitely generated, being finitely presented and being residually finite under direct products in the context of different types of algebraic structures. The structures considered include…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin…
We show that including degrees of a particular kind of provability in the search target for any theorem-prover in sufficiently powerful formal systems over finite-sized statements preserves well-definition and a sufficient consistency while…
We prove a connexity theorem for abelian varieties in characteristic $0$: if $X$ is an abelian variety and $V\rightarrow X$ and $W\rightarrow X$ two morphisms, then, under certain hypotheses, the fiber product of $V$ and $W$ over $X$ is…
We consider the question of the boundedness of matrix products $A_{n}B_{n}\cdots A_{1}B_{1}$ with factors from two sets of matrices, $A_{i}\in\mathscr{A}$ and $B_{i}\in\mathscr{B}$, due to an appropriate choice of matrices $\{B_{i}\}$. It…
We prove that an irreducible lattice acting on a product of two or more locally finite, biregular trees is finitely generated.
Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allowed. We use log geometry to formulate a new sparsity…
In this note, we characterise when the kernel of a rational character of a right-anlged Artin group, also known as generalised Bestiva-Brady group, is finitely generated and finitely presented. In these cases, we exhibit a finite generating…