Related papers: Forking in Short and Tame Abstract Elementary Clas…

The Tate conjecture has two parts: i) Tate classes are linear combination of algebraic classes, ii) semisimplicity of Galois representations (for smooth projective varieties). B. Moonen proved that i) implies ii) in characteristic 0, using…

Baez asks whether the Euler characteristic (defined for spaces with finite homology) can be reconciled with the homotopy cardinality (defined for spaces with finite homotopy). We consider the smallest infinity category…

In the present paper we shall prove that countable \omega-categorical simple CM-trivial theories and countable \omega-categorical simple theories with strong stable forking are low. In addition, we observe that simple theories of bounded…

A self-contained exposition is given of the topological and Galois-theoretic properties of the category of combinatorial 1-complexes, or graphs, very much in the spirit of Stallings. A number of classical, as well as some new results about…

We prove: $\mathbf{Theorem}$ Let $K$ be a universal class. If $K$ is categorical in cardinals of arbitrarily high cofinality, then $K$ is categorical on a tail of cardinals. The proof stems from ideas of Adi Jarden and Will Boney, and also…

Let $L/K$ be a tame and Galois extension of number fields with group $G$. It is well-known that any ambiguous ideal in $L$ is locally free over $\mathcal{O}_KG$ (of rank one), and so it defines a class in the locally free class group of…

An expression $E(X_{1},...,X_{n})$ built using union, intersection, and complements is called inclusion-exclusion-like if, like the union in the exclusion-inclusion principle, there are constants $c_{1},c_{2},...,c_{n}$ so that for any…

A tournament is said to have the $S_k$-property if, for any set of $k$ players, there is another player who beats them all. Minimum tournaments having this property have been explored very well in the 1960's and the early 1970's. In this…

This paper provides a nonparametric analysis for several classes of models, with cases such as classical measurement error, regression with errors in variables, factor models and other models that may be represented in a form involving…

We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between…

We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain roots of unity. In doing so, we find criteria which allow…

Let $F$ be a field with characteristic $\neq 2$. We show that $F$ is a nonrigid field if and only if certain small 2-groups occur as Galois groups over $F$. These results provide new "automatic realizability" results for Galois groups over…

We provide a differential-algebraic description of forking independence in the stable theory DCF$_{p,m}$ of differentially closed fields of characteristic $p>0$ with $m$-many commuting derivations. As a by-product of this description, we…

Monadic stability and the more general monadic dependence (or NIP) are tameness conditions for classes of logical structures, studied in the 80's in Shelah's classification program in model theory. They recently emerged in algorithmic and…

We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois deformation rings for unramified extensions of $\mathbb{Q}_p$ with small regular…

In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models. An posible generalization of the Lob's theorem is considered.Main results is: (1) let $k$ be an inaccessible…

We propose a generalisation of the Cameron-Erdos conjecture for sum-free sets to arbitrary non-translation invariant linear equations over Z in three or more variables and, using well-known methods from graph theory, prove a weak form of…

In this paper we focus on functions of the form $A^n\rightarrow \mathcal{P}(B)$, for possibly different arbitrary non-empty sets $A$ and $B$, and where $\mathcal{P}(B)$ denotes the set of all subsets of $B$. These mappings are called…

Let $R$ be a complete discrete valuation ring with residue characteristic $p>0$. In this note we give an example of a Galois cover $f:Y\to X$ between flat and normal formal $R$-schemes of finite type which is \'etale above the generic fibre…

Let $\mathbf{k}$ be an algebraically closed field of characteristic $\geq 7$ or zero. Let $\mathcal{A}$ be a tame order of global dimension $2$ over a normal surface $X$ over $\mathbf{k}$ such that…