Let K = k(C) be the function field of a curve over a field k and let X be a smooth, projective, separably rationally connected K-variety with X(K) 6= ∅. Under the assumption that X admits a smooth projective model π : X → C, we prove the following weak approximation results: (1) if k is a large field, then X(K) is Zariski dense; (2) if k is an infinite algebraic extension of a finite field, the...

Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field  with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.

In this article we consider different approaches for constructing maximal abelian extensions local and global geometric fields. The Lubin–Tate theory plays key role in the extension construction case of fields, Drinfeld modules are particular interest. paper simpliest special projective line which is called Carlitz module. introduction, provide motivation a brief historical background on topics...

‎Let $C$ be a semidualizing module‎. ‎We first investigate the properties of‎ ‎finitely generated $G_C$-projective modules‎. ‎Then‎, ‎relative to $C$‎, ‎we introduce and study the rings over which‎ ‎every submodule of a projective (flat) module is $G_C$-projective (flat)‎, ‎which we call $C$-Gorenstein (semi)hereditary rings‎. ‎It is proved that every $C$-Gorenstein hereditary ring is both cohe...

We prove that the stabiliser group GX of the Segre variety product in PG(V ) of three projective lines over a field F has four orbits on singular points of PG(V ), and that GX has five orbits on points of PG(V ) if F is finite.

We present a polynomial-time algorithm for computing the zeta function of a smooth projective hypersurface of degree d over a finite field of characteristic p, under the assumption that p is a suitably small odd prime and does not divide d. This improves significantly upon an earlier algorithm of the author and Wan which is only polynomial-time when the dimension is fixed.

It is shown that good linear [n, k, d] codes over a finite field GF(q) can be constructed by concatenating the generator matrices of Reed-Solomon codes. For the first interesting case of k = 3, it is shown that many of the codes obtained via projective geometry techniques can readily be obtained via the proposed algebraic approach.

We show that a principal G bundle on a smooth projective curve over a finite field is strongly semistable if and only if it is defined by a representation of the fundamental group scheme of the curve into G. MSC 2000 classification:14-XX

We prove that the stabiliser group GX of the Segre variety product in PG(V ) of three projective lines over a field F has four orbits on singular points of PG(V ), and that GX has five orbits on points of PG(V ) if F is finite.

Let G be a finite group acting faithfully on an irreducible non-singular projective curve defined over an algebraically closed field F . Does every G-invariant divisor class contain a Ginvariant divisor? The answer depends only on G and not on the curve. We answer the same question for degree 0 divisor (classes). We investigate the question for cycles on varieties.