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摘要翻译：
将有限群G表示的形式（混合特征）形变函子D看作正特征完美域k上幂级数环k[[t]]的自同构。假定G的作用是弱分枝的，即第二分枝群是平凡的。这类表示的例子可以通过群对普通曲线的作用来提供：分支群对这类曲线上任意点的完备局部环的作用是弱分支的。我们证明了只有当k具有特征2，G是二阶或同构于Klein群时，才会有这样的D不是亲可表示的。此外，我们还证明了其中只有第一个具有非亲表示的等分变形函子。
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英文标题：
《Which weakly ramified group actions admit a universal formal
deformation?》
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作者：
Jakub Byszewski and Gunther Cornelissen
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最新提交年份：
2008
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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：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
Consider a formal (mixed-characteristic) deformation functor D of a representation of a finite group G as automorphisms of a power series ring k[[t]] over a perfect field k of positive characteristic. Assume that the action of G is weakly ramified, i.e., the second ramification group is trivial. Examples of such representations are provided by a group action on an ordinary curve: the action of a ramification group on the completed local ring of any point on such a curve is weakly ramified. We prove that the only such D that are not pro-representable occur if k has characteristic two and G is of order two or isomorphic to a Klein group. Furthermore, we show that only the first of those has a non-pro-representable equicharacteristic deformation functor.
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PDF链接：
https://arxiv.org/pdf/0708.3279
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