Related papers: A note on Hermitian forms and Maschke's Theorem

We give examples of sequences of smooth non-isotrivial curves for every genus at least two, defined over a rational function field of positive characteristic, such that the (finite) number of rational points of the curves in the sequence…

In this paper we prove a version of Grothendieck's section conjecture for the restriction of the universal complete curve over M_{g,n}, g > 4, to the function field k(M_{g,n}) where k is, for example, a number field. In this version, the…

To every covering of curves, we associate several varieties having the same field of moduli and same fields of definition. We deduce examples of curves having Q (the field of rationals) as field of moduli, that admit models over any…

Working over imperfect fields, we give a comprehensive classification of genus-one curves that are regular but not geometrically regular, extending the known case of geometrically reduced curves. The description is given intrinsically, in…

The purpose of this note is to give a short, selfcontained proof of the following result: A complex surface which is diffeomeorphic to a rational surface is rational.

Suppose that $F$ is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve with positive self-intersection. We prove that if there exists a non-constant meromorphic function on $F$, then the…

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

Given a smooth cubic hypersurface $X$ over a finite field of characteristic greater than 3 and two generic points on $X$, we use a function field analogue of the Hardy-Littlewood circle method to obtain an asymptotic formula for the number…

We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. The starting point of this research was the need to understand in a sound mathematical framework some…

A generalization of the Heisenberg algebra has been recently constructed. This generalized algebra has a characteristic function which depends on one of its generators. When this function is linear, $qJ_0+s$, it is possible to construct a…

We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…

This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a…

In this short note we try to generalize the Clemens-Griffiths criterion of non-rationality for smooth cubic threefolds to the case of smooth cubic fourfolds.

There are theorems in the literature which are referred as Maschke type theorems, because of the attempt to generalize Maschke's classical theorem. Our remark is that all these theorems are in fact providing sufficient conditions for the…

We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets…

We give a simple proof of the splitting lemma in singularity theory, also known as generalized Morse lemma, for formal power series over arbitrary fields. Our proof for the uniqueness of the residual part in any characteristic is new and…

We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields. The simplest proposed theory is defined over arbitrary finite fields and loses the notion of unitaries. This makes such…

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.