p-RANKS AND AUTOMORPHISM GROUPS OF ALGEBRAIC CURVES
نویسنده
چکیده
Let X be an irreducible complete nonsingular curve of genus g over an algebraically closed field k of positive characteristic p. If g > 2, the automorphism group Aut(X) of X is known to be a finite group, and moreover its order is bounded from above by a polynomial in g of degree four (Stichtenoth). In this paper we consider the p-rank -7 of X and investigate relations between if and Aut(X). We show that 1 affects the order of a Sylow p-subgroup of Aut(X) (§3) and that an inequality |Aut(X)| < 84(g — l)g holds for an ordinary (i.e. i = g) curve X (§4).
منابع مشابه
On large automorphism groups of algebraic curves in positive characteristic
In his investigation on large K-automorphism groups of an algebraic curve, Stichtenoth obtained an upper bound on the order of the first ramification group of an algebraic curve X defined over an algebraically closed field of characteristic p. Stichtenoth’s bound has raised the problem of classifying all K-automorphism groups G of X with the following property: There is a point P ∈ X for which ...
متن کاملAUTOMORPHISM GROUP OF GROUPS OF ORDER pqr
H"{o}lder in 1893 characterized all groups of order $pqr$ where $p>q>r$ are prime numbers. In this paper, by using new presentations of these groups, we compute their full automorphism group.
متن کاملElliptic factors in Jacobians of hyperelliptic curves with certain automorphism groups
We decompose the Jacobian variety of hyperelliptic curves up to genus 20, defined over an algebraically closed field of characteristic zero, with reduced automorphism group A4, S4, or A5. Among these curves is a genus 4 curve with Jacobian variety isogenous to E2 1 × E2 2 and a genus 5 curve with Jacobian variety isogenous to E5, for E and Ei elliptic curves. These types of results have some in...
متن کاملDarren Glass : Description of Current Research Interests Spring 2008
My research interests are generally in the areas of algebraic geometry, number theory, and Galois theory. My dissertation and some of the research at that time focussed on profinite Galois groups ([2]) and ε-constants associated to arithmetic schemes ([5], [6]), and I have continued this work with a more recent paper on the De Rham cohomology of elliptic curves ([9]). However, most of my recent...
متن کاملIdempotent relations and generalized p - ranks of curves ∗
Let Y be a smooth projective irreducible curve defined over a finite field F q. We assume that G is a finite subgroup of the automorphism group of Y whose order divides q − 1. We show that relations among idempotents corresponding to the irreducible characters of subgroups H of G imply similar relations among generalized pranks of Y. We also relate this result to the realization of finite group...
متن کامل