Principal bundles over a curve in positive characteristic, II
نویسندگان
چکیده
منابع مشابه
Moduli of principal bundles in positive characteristic
1. Let G be a semisimple algebraic group defined over an algebraically closed field k of characteristic p. In this article, we construct the moduli space of semistable principal G bundles on a smooth projective curve X over k, of genus g ≥ 2. When the characteristic is zero, for example the field of complex numbers, these moduli spaces were first constructed by A. Ramanathan (see [8], [9]). Lat...
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Let H be a semisimple algebraic group and let X be a smooth projective curve defined over an algebraically closed field k. One of the important problems in the theory of principal H-bundles on X is the construction of the moduli spaces of semistable H-bundles when the characteristic of k is positive. Over fields of characteristic 0 this work was done by A.Ramanathan (cf.[R1]). For principal GL(...
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Let X be an irreducible smooth projective curve over an algebraically closed field k of characteristic p, with p > 5. Let G be a connected reductive algebraic group over k. Let H be a Levi factor of some parabolic subgroup of G and χ a character of H. Given a reduction EH of the structure group of a G-bundle EG to H, let Eχ be the line bundle over X associated to EH for the character χ. If G do...
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Let (X, ω) be a compact connected Kähler manifold of complex dimension d and EG −→ X a holomorphic principal G–bundle, where G is a connected reductive linear algebraic group defined over C. Let Z(G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P ⊂ G and a holomorphic reduction of structure group EP ⊂ EG to P , such that ...
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Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2005
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2004.10.002