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A Candidate for the Abelian Category of Mixed Elliptic Motives

Published online by Cambridge University Press:  15 November 2013

Owen Patashnick
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Abstract

In this work, we s uggest a defnition for the category of mixed motives generated by the motive h1 (E) for E an elliptic curve without complex multiplication. We then compute the cohomology of this category. Modulo a strengthening of the Beilinson-Soulé conjecture, we show that the cohomology of our category agrees with the expected motivic cohomology groups. Finally for each pure motive (Symnh1 (E)) (–1) we construct families of nontrivial motives whose highest associated weight graded piece is (Symnh1 (E)) (–1).

Keywords

Keywords arithmetic geometrycohomologyalgebraic cyclesK-theorymotiveLie algebras and their representationselliptic curveselliptic polylogarithmL-function14C2514C3014G9914Q0514F4214C2519D9913D1517B4518E1518F3014H5211G5511G4014G10
Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 3 , December 2013 , pp. 569 - 600
Copyright
Copyright © ISOPP 2013 

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