Let K be the function field of an algebraic curve C defined over a finite field Fq. Let V ⊂ PK be a projective variety which is a union of lines. We prove a general result computing the number of rational points of bounded height on V/K. We first compute the number of rational points on a general line defined over K, and then sum over the lines covering V . Mathematics Subject Classification: 1...

Let $K$ be the function field of a curve over finite odd characteristic. We investigate using $L$-functions Galois extensions to effectively recover $K$. When is projective line with four rational points removed, we show how use ray class removed up automorphisms line. plane curve, equation that Artin-Schreier

We give the first examples of nef line bundles on smooth projective varieties over finite fields which are not semi-ample. More concretely, we find smooth curves on smooth projective surfaces over finite fields such that the normal bundle has degree zero, but no positive multiple of the curve moves in a family of disjoint curves. This answers questions by Keel and Mumford. The proof uses an obs...

where St and S2 are projective representations of G. An irreducible projective representation is one that is not reducible. In this paper, we study the degrees of irreducible projective representations of a finite group G over an algebraically closed field K. In Theorem 2, we require further that char KJ(\G\. The degree of an irreducible projective representation of a finite group G, over the c...

Let K = Fq be a finite field. We introduce a family of projective Reed-Mullertype codes called projective Segre codes. Then we study their basic parameters and show that they are direct products of projective Reed-Muller-type codes. It turns out that the direct product of two projective Reed-Muller-type codes is again a projective Reed-Muller-type code. As a consequence we recover some results ...

1.1. Let S be a finite set of places of a finite field extension L of a number field K, containing all infinite places. Let E be a vector space over K of dimension N + 1. For v ∈ S, let lv0, · · · , lvN be linearly independent vectors in E ⊗K L. Choose a projective subvariety X defined over K, embedded into the projective space P(E∨) of lines of the dual vector space E∨. Consider the system of ...