Related papers: Local character of Kim-independence

Assume that $\mathcal{P}$ is a topological property of a space $X$, then we say that $X$ is {\it dense-$\mathcal{P}$} if each dense subset of $X$ has the property $\mathcal{P}$. In this paper, we mainly discuss dense subsets of a space $X$,…

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…

Fix a field $K$. We show that $K$ is large if and only if some elementary extension of $K$ is the fraction field of a henselian local domain which is not a field. The proof uses a new result about the \'etale-open topology over $K$: if $K$…

We study the Knapp-Stein R-groups of the inner forms of SL(N) over a non-archimedean local field of characteristic zero, by using restriction from the inner forms of GL(N). As conjectured by Arthur, these R-groups are then shown to be…

We show that the theory $T_{\log}$ of the asymptotic couple of the field of logarithmic transseries is distal. As distal theories are NIP (= the non-independence property), this provides a new proof that $T_{\log}$ is NIP. Finally, we show…

We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set $A$ of $n$ real numbers such that $|A-A|=n^{\log_2 3}$ and that every subset $A'\subseteq A$ of size…

Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies $ \mathscr L $-$ \Pi $-property in $ G $ if $ | G / K : N _{G / K} (HK/K)| $ is a $ \pi (HK/K) $-number for all maximal $ G $-invariant subgroup $ K $ of $ H^{G}…

Gcharacter tables of a finite group G were defined before. These tables can be very useful to obtain certain structural information of a normal subgroup from the character table of G. We analyze certain structural properties of normal…

We show that relative Property (T) for the abelianization of a nilpotent normal subgroup implies relative Property (T) for the subgroup itself. This and other results are a consequence of a theorem of independent interest, which states that…

We consider local densities for $p$-adic quaternion hermitian forms (hermitian forms over a division quaternion algebra over a ${\mathfrak p}$-adic field $k$). The author has studied such forms in connection with spherical functions on the…

The aim of this note is to determine whether certain non-o-minimal expansions of o-minimal theories which are known to be NIP, are also distal. We observe that while tame pairs of o-minimal structures and the real field with a discrete…

The randomization of a complete first order theory $T$ is the complete continuous theory $T^R$ with two sorts, a sort for random elements of models of $T$, and a sort for events in an underlying atomless probability space. We study…

A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…

We characterize the $k$-torsion freeness of the module of differentials of order $n$ of a point of a hypersurface in terms of the singular locus of the corresponding local ring.

We characterize when a subfactor $N\subseteq M$ is oracle computable relative to a presentation of the ambient factor $M$ in terms of computability of the Jones basic construction, in terms of computable Pismner-Popa bases, and in terms of…

In this article we study various forms of $\ell$-independence (including the case $\ell=p$) for the cohomology and fundamental groups of varieties over finite fields and equicharacteristic local fields. Our first result is a strong form of…

Let $S$ be KLT threefold singularity over an algebraically closed field of positive characteristic $p>5$. We prove that its local \'etale fundamental group is tame and finite. Further, we show that every finite unipotent torsor over a big…

We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of $NIP$ (not the independence property), continuing aspects of math.LO/0607442. Among key results are: (i) if $p = tp(b/A)$ does not fork…

We develop a local model theory for moduli stacks of $2$-dimensional non-scalar tame potentially Barsotti--Tate Galois representations of the Galois group of an unramified extension of $\mathbb{Q}_p$. We derive from this explicit…

For a finite group G of Lie type and a prime p, we compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic,…