Rigid Cohomology over Laurent Series Fields
Rigid Cohomology over Laurent Series Fields
复制标题
洛朗级数域上的刚性上同调
DOI：
10.1007/978-3-319-30951-4
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Lazda C
中科院分区：
文献类型：
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作者：
Lazda C
这本书的灵感来自于我们希望更好地理解积极特征的时期地图，就像金教授在研究理性点的程序中使用的那样。我们很快意识到，目前严重缺乏的是正特征局部域（即局部函数域）上的变异的p进上同的鲁棒图，这里的结果包括我们为这样一个理论提供基础的尝试。我们的方法的灵感和模型（毫不奇怪）是贝特洛的刚性上同论，在某种意义上，这里的关键见解主要是做出正确的定义，而不是证明全新的结果。本书的关键观察是，一旦这些定义到位，许多关于刚性上同调的现有文献，它的构造，以及它的大多数基本性质的证明，如有限维数和上同调下降，可以应用于比迄今为止普遍认为的更一般的情况。
This book grew out of our desire to better understand period maps in positive characteristic, analogous to those used by Kim in his program to study rational points. We very quickly realised that what was currently sorely lacking was a robust picture of p-adic cohomology for varieties over positive characteristic local fields (ie local function fields), and the results here consist of our attempt to provide the foundations for such a theory.The inspiration and model for our approach is (unsurprisingly) Berthelot’s theory of rigid cohomology, and in some sense the key insights here are mostly that of making the right definitions rather than proving completely new results. The crucial observation of this book is that once these definitions are in place, much of the existing literature on rigid cohomology, its construction, and most of the proofs of its fundamental properties such as finite dimensionality and cohomological descent, can be applied in more general situations than have generally been considered to date.