Related papers: Valued difference fields and NTP2

We prove that the (elementary) class of differential-difference fields in characteristic $p>0$ admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic…

We prove that a valued field of positive characteristic $p$ that has only finitely many distinct Artin-Schreier extensions (which is a property of infinite NTP$_2$ fields) is dense in its perfect hull. As a consequence, it is a deeply…

A long-standing conjecture asserts that every finite non-abelian $p$-group has a non-inner automorphism of order $p$. In this paper, we settle the conjecture for a finite $p$-group ($p >2$) of nilpotency class $n$ with certain conditions.

We explain that a new theorem of Deligne on symmetric tensor categories implies, in a straightforward manner, that any finite dimensional triangular Hopf algebra over an algebraically closed field of characteristic zero has Chevalley…

We describe the groups of inner and outer automorphisms of the free metabelian nilpotent Lie algebra of finite rank over a field of characteristic 0. To obtain this result we first describe the groups of inner and continuous outer…

We generalize the positive solution of the Frobenius conjecture and refinements thereof by studying the structure of groups that admit a fix-point-free automorphism satisfying an identity. We show, in particular, that for every polynomial…

We classify Frobenius forms, a special class of homogeneous polynomials in characteristic $p>0$, in up to five variables over an algebraically closed field. We also point out some of the similarities with quadratic forms.

We classify finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradcial is isomorphic to the smallest non-pointed basic Hopf algebra, under the assumption that the diagrams are strictly…

In analogy with the Riemann zeta function at positive integers, for each finite field F_p^r with fixed characteristic p we consider Carlitz zeta values zeta_r(n) at positive integers n. Our theorem asserts that among the zeta values in…

Topological quantum field theories (TQFTs) are symmetric monoidal functors out of cobordism categories. In dimension two, oriented TQFTs are famously classified by commutative Frobenius algebras. In the unoriented setting, the…

In this paper we describe graded automorphisms and antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of charcteristic different from 2.

Following ideas of G. Moore and G. Segal, we explicitly construct a G-equivariant topological field theory from an arbitrary Frobenius algebra equipped with a twisted action of a finite group G.

Conditions are given under which an infinitesimal automorphism of a torsion-free connection preserving a symplectic form is necessarily a symplectic vector field. An example is given of a compact symplectic manifold admitting a flat…

We generalize previous results about stable domination and residue field domination to henselian valued fields of equicharacteristic 0 with bounded Galois group, and we provide an alternate characterization of stable domination in…

Starting with a unit-preserving normal completely positive map L: M --> M acting on a von Neumann algebra - or more generally a dual operator system - we show that there is a unique reversible system \alpha: N --> N (i.e., a complete order…

We construct and describe the basic properties of a family of semifields in characteristic $2.$ The construction relies on the properties of projective polynomials over finite fields. We start by associating non-associative products to each…

For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…

A $d$-dimensional invertible topological field theory is a functor from the symmetric monoidal $(\infty,n)$-category of $d$-bordisms (embedded into $\mathbb{R}^\infty$ and equipped with a tangential $(X,\xi)$-structure) which lands in the…

Let $A$ be an $n$-dimensional algebra over a field $k$ and $a(A)$ its quantum symmetry semigroup. We prove that the automorphisms group ${\rm Aut}_{\rm Alg} (A)$ of $A$ is isomorphic to the group $U \bigl( G(a (A)^{\rm o} ) \bigl)$ of all…

We characterize those Lie groups, and algebraic groups over a local field of characteristic zero, whose first reduced L^p-cohomology is zero for all p>1, extending a result of Pansu. As an application, we obtain a description of…