上同调对数板上的双延拓与耦合
Prolongement de biextensions et accouplements en cohomologie log plate
摘要：
利用对数格式的语言，研究了光滑交换群格式的双扩张通过乘法群的推广问题。这是格罗滕迪克在SGA 7中首次考虑的。我们发现，这个问题承认一个解决方案的范畴内的层加藤的日志平坦的拓扑结构，在对比可以观察到的使用fppf拓扑结构，单值障碍定义的Grothendieck。特别地，在阿贝尔簇及其对偶的情况下，可以将Weil双扩张推广到整个Néron模型。这使我们能够定义一个配对的点，结合类组配对定义的马祖尔和泰特和格罗滕迪克的monodromy配对。
英文摘要：
We study, using the language of log schemes, the problem of extending biextensions of smooth commutative group schemes by the multiplicative group. This was first considered by Grothendieck in SGA 7. We show that this problem admits a solution in the category of sheaves for Kato's log flat topology, in contradistinction to what can be observed using the fppf topology, for which monodromic obstructions were defined by Grothendieck. In particular, in the case of an abelian variety and its dual, it is possible to extend the Weil biextension to the whole Néron model. This allows us to define a pairing on the points which combines the class group pairing defined by Mazur and Tate and Grothendieck's monodromy pairing.
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