摘要翻译:
本文研究了完全离散值域上American分支阿贝尔簇$a$的一个迹公式,它用$a$的$Ell$-adic上同调上的Galois作用表示了$a$的N\'eron模型的特殊纤维的Euler特性。如果a$具有纯加性约简,则迹公式对n\'eron模型的特殊光纤的连通分量数产生上同调解释。
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英文标题:
《Trace formula for component groups of N\'eron models》
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作者:
Johannes Nicaise
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最新提交年份:
2009
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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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英文摘要:
We study a trace formula for tamely ramified abelian varieties $A$ over a complete discretely valued field, which expresses the Euler characteristic of the special fiber of the N\'eron model of $A$ in terms of the Galois action on the $\ell$-adic cohomology of $A$. If $A$ has purely additive reduction, the trace formula yields a cohomological interpretation for the number of connected components of the special fiber of the N\'eron model.
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PDF链接:
https://arxiv.org/pdf/0901.1809