Local-global principles for Galois cohomology
Local-global principles for Galois cohomology
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伽罗瓦上同调的局部全局原理
DOI：
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发表时间：
2012
期刊：
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通讯作者：
D. Krashen
中科院分区：
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作者：
D. Harbater;Julia Hartmann;D. Krashen
本文证明了在完全离散值域上定义曲线函数域$F$上伽罗瓦上同群的局部-全局原理。我们特别证明了这些原理对于$H^n(F, Z/mZ(n-1))$，对于所有$n>1$都成立。这是由Kato和其他人的工作所激发的，这些原则在相关的案例中被证明是n=3的。结合上同调不变量，我们得到了$F$上的环量和相关代数结构的局部-全局原理。我们的论证依赖于补丁理论和布洛赫-加藤猜想。
This paper proves local-global principles for Galois cohomology groups over function fields $F$ of curves that are defined over a complete discretely valued field. We show in particular that such principles hold for $H^n(F, Z/mZ(n-1))$, for all $n>1$. This is motivated by work of Kato and others, where such principles were shown in related cases for $n=3$. Using our results in combination with cohomological invariants, we obtain local-global principles for torsors and related algebraic structures over $F$. Our arguments rely on ideas from patching as well as the Bloch-Kato conjecture.