摘要翻译:
我们证明了场的Milnor k-理论mod$p$中的运算是由除幂运算跨越的。给出了除幂运算的一个显式公式,并将其推广到一些新的情形,我们确定了对于所有域$K$和所有素数$P$,所有运算$K^M_I/P\到K^M_J/P$在基域$K$上的域扩展交换。此外,我们还讨论了积分情形,并确定了域上光滑格式的运算$k^m_i/p\到k^m_j/p$。
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英文标题:
《Operations in Milnor K-theory》
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作者:
Charles Vial
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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:K-Theory and Homology K-理论与同调
分类描述:Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
代数和拓扑K-理论,与拓扑的关系,交换代数和算子代数
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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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英文摘要:
We show that operations in Milnor K-theory mod $p$ of a field are spanned by divided power operations. After giving an explicit formula for divided power operations and extending them to some new cases, we determine for all fields $k$ and all prime numbers $p$, all the operations $K^M_i/p \to K^M_j/p$ commuting with field extensions over the base field $k$. Moreover, the integral case is discussed and we determine the operations $K^M_i/p \to K^M_j/p$ for smooth schemes over a field.
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PDF链接:
https://arxiv.org/pdf/0812.0481