Related papers: Artin-Schreier extensions in NIP and simple fields

Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with…

We classify simple groups that act by birational transformations on compact complex K\"ahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective…

Given a compact, oriented surface $S$ of finite genus and finitely many boundary components, we provide examples of finite covers $\tilde{S}$ of $S$ and non-simple closed curves $\gamma$ on $S$ which lifts to simple closed curves on…

It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that…

Let $K$ be a complete non-Archimedean field $K$ with separated power series, treated in the analytic Denef--Pas language. We prove the existence of definable retractions onto an arbitrary closed definable subset of $K^{n}$, whereby…

We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…

We prove the boundedness of $n$-complements for surface pairs in a generalized case without restrictions on multiplicities or the Fano type assumption.

We show that the Fargues--Fontaine curve associated to an algebraically closed field of characteristic p is geometrically simply connected; that is, its base extension from Q_p to any complete algebraically closed overfield admits no…

Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group $G$ factors through a projective representation of $G$, except for some groups of Lie…

Hobby has recently shown that almost all finite hyperfields of even order fail to be the quotient of a field. Using a probabilistic argument, we extend this result to all orders: a finite hyperfield is almost always non-quotient. This…

This paper shows that in general, difference fields do not have a difference closure. However, we introduce a stronger notion of closure (kappa-closure), and show that every algebraically closed difference field K of characteristic 0, with…

We prove the following generalization of an example of Hartshorne: Let k be a field, n=4, R = k[[X1,...,Xn]], I = (X1,...,Xn-2)R and p\in R a prime element such that p\in(Xn-1,Xn)R. Then H^{n-2}_I (R/pR) is not artinian.

All counterexamples of Pinchuk type to the strong real Jacobian conjecture are shown to have rational function field extensions of degree six with no nontrivial automorphisms.

We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of…

We study the codegree isomorphism problem for finite simple groups. In particular, we show that such a group is determined by the codegrees (counting multiplicity) of its irreducible characters. The proof is uniform for all simple groups…

We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the…

The main result of this paper is that if E is a field extension of finite odd degree over a real field Q, and if E is a repeated radical extension of Q, then every intermediate field is also a repeated radical extension of Q. This paper…

We study weak approximation for Ch\^{a}telet surfaces over number fields when all singular fibers are defined over rational points. We consider Ch\^{a}telet surfaces which satisfy weak approximation over every finite extension of the ground…

Let H be an infinite-dimensional Taft algebra over an algebraically closed field k of characteristic 0. We find all the simple Yetter-Drinfeld modules V over H, and classifies those V with B(V) is finite-dimensional.

We prove that any large even Artin group is poly-free and that any even Artin group based on a triangle graph is also poly-free.