Related papers: Around Podewski's conjecture

K. Harada conjectured for any finite group $G$, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when $G$ is the general linear group over a finite…

A result of Pyber states that every finite group $G$ contains an abelian subgroup whose order is quasi-polynomially large in $\lvert G\rvert$. We prove a similar result for $K$-approximate subgroups of solvable groups under only modest…

We study the algebraic closure of $\mathbb K(\!(x)\!)$, the field of power series in several indeterminates over a field $\mathbb K$. In characteristic zero we show that the elements algebraic over $\mathbb K(\!(x)\!)$ can be expressed as…

Kaplanski's Zero Divisor Conjecture envisions that for a torsion-free group G and an integral domain R, the group ring R[G] does not contain non-trivial zero divisors. We define the length of an element a in R[G] as the minimal non-negative…

Let A be an abelian variety over a number field k. We show that weak approximation holds in the Weil-Ch\^atelet group of A/k but that it may fail when one restricts to the n-torsion subgroup. This failure is however relatively mild; we show…

In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…

The conjecture of Kosniowski asserts that if the circle acts on a compact unitary manifold $M$ with a non-empty fixed point set and $M$ does not bound a unitary manifold equivariantly, then the dimension of the manifold is bounded above by…

We introduce and develop the model-theoretic notions of absolute connectedness and type-absolute connectedness for groups. We prove that groups of rational points of split semisimple linear groups (that is, Chevalley groups) over arbitrary…

Conjecture A of \cite{EM14} predicts the equality between the smallest positive height of the irreducible characters in a $p$-block of a finite group and the smallest positive height of the irreducible characters in its defect group. Hence,…

Let G be a linear algebraic group defined over a field k. We prove that, under mild assumptions on k and G, there exists a finite k-subgroup S of G such that the natural map H^1(K, S) -> H^1(K, G) is surjective for every field extension…

We prove that many of the results of the LMMP hold for $3$-folds over fields of characteristic $p>5$ which are not necessarily perfect. In particular, the existence of flips, the cone theorem, the contraction theorem for birational extremal…

Restriction is a natural quasi-order on $d$-way tensors. We establish a remarkable aspect of this quasi-order in the case of tensors over a fixed finite field -- namely, that it is a well-quasi-order: it admits no infinite antichains and no…

We show that Zilber's conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the first-order types in…

Let $ M_0 $ denote either the field structure $ \mathbb{Q}_p $ of $ p $-adic numbers, or an $o$-minimal expansion of the field structure $ \mathbb{R} $ of real numbers. We investigate the minimal flows and Ellis groups of definable groups…

In this article we continue with the study started in [1] of nearly Frobenius structures in some representative families of finite dimensional algebras, as the radical square zero algebras, string algebras and the toupie algebras. We prove…

We study groups and rings definable in d-minimal expansions of ordered fields. We generalize to such objects some known results from o-minimality. In particular, we prove that we can endow a definable group with a definable topology making…

We extend some results of Carderi and Le Ma\^itre on full groups in the probability context to the infinite measure one: there exists at most one Polish group topology (refining the weak topology and coarser than the uniform topology) on an…

A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…

We study the Borel subsets of the plane that can be made closed by refining the Polish topology on the real line. These sets are called potentially closed. We first compare Borel subsets of the plane using products of continuous functions.…

We prove that the geometric Bogomolov conjecture for any abelian varieties is reduced to that for nowhere degenerate abelian varieties with trivial trace. In particular, the geometric Bogomolov conjecture holds for abelian varieties whose…