Related papers: On Belyi's Theorems in Positive Characteristic

We extend Poonen's Bertini theorem over finite fields to Taylor conditions arising from locally free quotients of the sheaf of differentials on projective space. This is motivated by a result of Bilu and Howe in the motivic setting that…

It has been conjectured that every algebraic curve may be defined either over its field of moduli or over an extension of degree two of it. In this paper we provide a negative answer to it by giving examples of hyperelliptic curves which…

Let $X$ be a locally compact Abelian group, $Y$ be its character group. Following A. Kagan and G. Sz\'ekely we introduce a notion of $Q$-independence for random variables with values in $X$. We prove group analogues of the Cram\'er,…

We discuss recent progress on topological Helly-type theorems and their variants. We provide an overview of two different proof techniques, one based on the nerve lemma, while the other on non-embeddability.

Let p:C' -> C be an unramified double covering of irreducible smooth curves and let P be the attached Prym variety. We prove the schematic theta-dual equalities in the Prym variety T(C')=V^2 and T(V^2)=C', where V^2 is the Brill-Noether…

A generalization of Serre's Conjecture asserts that if $F$ is a totally real field, then certain characteristic $p$ representations of Galois groups over $F$ arise from Hilbert modular forms. Moreover it predicts the set of weights of such…

The weak factorization theorem for birational maps is used to prove that for all nonnegative i the ith mod 2 Betti number of compact nonsingular real algebraic varieties has a unique extension to a "virtual Betti number" beta_i defined for…

Following ideas given by John Bell in a paper entitled \textit{Beables for quantum field theory}, we show that it is possible to obtain a realistic and deterministic interpretation of any quantum field-theoretic model involving Fermi…

The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…

By the Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of of $n$ independent random variables given another. When $n=2$ we prove analogues of this…

Let X be a projective variety which is covered by a family of rational curves of minimal degree. The classic bend-and-break argument of Mori asserts that if x and y are two general points, then there are at most finitely many curves in that…

We prove symplectic versions of Suslin's famous $n!$-theorem for algebras over quadratically closed perfect fields of characteristic $\neq 2$ and for algebras over finite fields of characteristic $\neq 2$.

Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We…

Over an arbitrary field of positive characteristic we construct an example of a locally finite variety of Lie algebras which does not have a finite basis of its polynomial identities. As a consequence we construct varieties of Lie algebras…

In this article, we prove a generalisation of the Mertens theorem for prime numbers to number fields and algebraic varieties over finite fields, paying attention to the genus of the field (or the Betti numbers of the variety), in order to…

Permutation polynomials over finite fields have taken an important role in vast areas in mathematics as well as engineering. Recently, Tu et al. gave some classes of complete permutation polynomials over finite fields of even…

We investigate exponential sums over singular binary quartic forms, proving an explicit formula for the finite field Fourier transform of this set. Our formula shares much in common with analogous formulas proved previously for other vector…

We use the theory of Harbater-Katz-Gabber curves to derive a generalization of the Hasse-Arf theorem for complete local field extensions in positive characteristic.

We show that each local field $\mathbb{F}_q((t))$ of characteristic $p > 0$ is characterised up to isomorphism within the class of all fields of imperfect exponent at most $1$ by (certain small quotients of) its absolute Galois group…

Under integral restrictions on dilatations, it is proved existence theorems for the degenerate Beltrami equations with two characteristics and, in particular, to the Beltrami equations of the second type that play a great role in many…