Lawson Homology for Abelian Varieties
Lawson Homology for Abelian Varieties
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DOI：
10.1515/forum-2012-0130
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发表时间：
2011-10
期刊：
影响因子：
--
通讯作者：
Wenchuan Hu
中科院分区：
文献类型：
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作者：
Wenchuan Hu
本文介绍了阿贝尔簇劳森同调的傅里叶-穆凯变换，并证明了阿贝尔簇劳森同调和形态上同调的反演定理。作为应用，我们受到 Beauville 关于 Chow 理论的著作的启发，获得了 Lawson 同调和具有有理系数的形态上同调群的直和分解。提出了 Chow 群的博维尔猜想的类比，并证明其与劳森同调的（弱）苏斯林猜想等效。提出了对劳森同调的过滤，推测它与阿贝尔簇的劳森同调的直和分解给出的过滤一致。此外，还获得了阿贝尔簇的精炼Friedlander-Lawson对偶定理。为了方便起见，我们在附录中总结了劳森同调论中的几个相关猜想。
In this paper we introduce the Fourier-Mukai transform for Lawson homology of abelian varieties and prove an inversion theorem for the Lawson homology as well as the morphic cohomology of abelian varieties. As applications, we obtain the direct sum decomposition of the Lawson homology and the morphic cohomology groups with rational coefficients, inspired by Beauville's works on the Chow theory. An analogue of the Beauville conjecture for Chow groups is proposed and is shown to be equivalent to the (weak) Suslin conjecture for Lawson homology. A filtration on Lawson homology is proposed and conjecturally it coincides to the filtration given by the direct sum decomposition of Lawson homology for abelian varieties. Moreover, a refined Friedlander-Lawson duality theorem is obtained for abelian varieties. We summarize several related conjectures in Lawson homology theory in the appendix for convenience.