Nori \(1\) -motives

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• 作者：Joseph Ayoub ; Luca Barbieri-Viale
• 关键词：19E15 ; 14F42 ; 14C30 ; 18G55 ; 13D09
• 刊名：Mathematische Annalen
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：361
• 期：1-2
• 页码：367-402
• 全文大小：406 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

Let \(\mathsf{{ EHM}}\) be Nori’s category of effective homological mixed motives. In this paper, we consider the thick abelian subcategory \(\mathsf{{ EHM}}_1\subset \mathsf{{ EHM}}\) generated by the \(i\) -th relative homology of pairs of varieties for \(i\in \{0,1\}\) . We show that \(\mathsf{{ EHM}}_1\) is naturally equivalent to the abelian category \({}^t\mathcal {M}_1\) of \(1\) -motives with torsion; this is our main theorem. Along the way, we obtain several interesting results. Firstly, we realize \({}^t\mathcal {M}_1\) as the universal abelian category obtained, using Nori’s formalism, from the Betti representation of an explicit diagram of curves. Secondly, we obtain a conceptual proof of a theorem of Vologodsky on realizations of \(1\) -motives. Thirdly, we verify a conjecture of Deligne on extensions of \(1\) -motives in the category of mixed realizations for those extensions that are effective in Nori’s sense.