摘要翻译:
本文介绍了一种研究群栈G在代数栈X上作用的显式方法。作为一个例子,我们详细研究了X=P(n_0,...,n_r)是任意基S上的加权射影栈的情形。为此,我们给出了加权射影一般线性2-群PGL(n_0,...,n_r)的自同构群栈的显式描述。作为应用,我们利用Colliot-Thelene的一个结果证明,对于任意基域k上的每一个线性代数群G(假定char(k)>0)是约化的,使得Pic}(G)=0),G在P(n_0,...,n_r)上的每一个作用都提升为G在a^{r+1}上的一个线性作用。
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英文标题:
《Group actions on algebraic stacks via butterflies》
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作者:
Behrang Noohi
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最新提交年份:
2013
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Quantum Algebra 量子代数
分类描述:Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
量子群,skein理论,运算代数和图解代数,量子场论
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英文摘要:
We introduce an explicit method for studying actions of a group stack G on an algebraic stack X. As an example, we study in detail the case where X=P(n_0,...,n_r) is a weighted projective stack over an arbitrary base S. To this end, we give an explicit description of the group stack of automorphisms of, the weighted projective general linear 2-group PGL(n_0,...,n_r). As an application, we use a result of Colliot-Thelene to show that for every linear algebraic group G over an arbitrary base field k (assumed to be reductive if char(k)>0) such that Pic}(G)=0, every action of G on P(n_0,...,n_r) lifts to a linear action of G on A^{r+1}.
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PDF链接:
https://arxiv.org/pdf/0704.1010