Klein-Four Covers of the Projective Line in Characteristic Two
نویسنده
چکیده
In this paper we examine curves defined over a field of characteristic 2 which are (Z/2Z)2-covers of the projective line. In particular, we prove which 2-ranks occur for such curves of a given genus and where possible we give explicit equations for such curves.
منابع مشابه
Reduction of covers and Hurwitz spaces
In this paper we study the reduction of Galois covers of curves, from characteristic zero to positive characteristic. The starting point is a recent result of Raynaud, which gives a criterion for good reduction for covers of the projective line branched at three points. We use the ideas of Raynaud to study the case of covers of the projective line branched at four points. Under some condition o...
متن کاملQuasi-projective covers of right $S$-acts
In this paper $S$ is a monoid with a left zero and $A_S$ (or $A$) is a unitary right $S$-act. It is shown that a monoid $S$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $S$-act is quasi-projective. Also it is shown that if every right $S$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...
متن کاملReduction and lifting of special metacyclic covers
Special covers are metacyclic covers of the projective line, with Galois group Z/p ⋊ Z/m, which have a specific type of bad reduction to characteristic p. Such covers arise in the study of the arithmetic of Galois covers of P with three branch points. Our results provide a classification of all special covers in terms of certain lifting data in characteristic p.
متن کاملThe existence totally reflexive covers
Let $R$ be a commutative Noetherian ring. We prove that over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.
متن کاملRings of Singularities
This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...
متن کامل