A candidate for the abelian category of mixed elliptic motives

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Abstract

In this paper we suggest a definition for the category of mixed motives generated by the motive h^1(E) for E an elliptic curve without complex multiplication. We then compute the cohomology of this category. Modulo a strengthening of the Beilinson-Soule conjecture, we show that the cohomology of our category agrees with the expected motivic cohomology groups. Finally for each pure motive (Sym^{n}h^1(E))(-1) we construct families of nontrivial motives whose highest associated weight graded piece is $Sym^{n}h^1(E))(-1).
Translated title of the contributionA candidate for the abelian category of mixed elliptic motives
Original languageEnglish
Pages (from-to)569
Number of pages600
JournalK-theory
Volume12
Issue number3
DOIs
Publication statusPublished - 15 Nov 2013

Bibliographical note

2 figures

Keywords

  • math.AG
  • math.KT
  • math.NT

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