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lie algebras and their representations

Journal of K-Theory (1)

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A Candidate for the Abelian Category of Mixed Elliptic Motives
Owen Patashnick
Journal:

Journal of K-Theory / Volume 12 / Issue 3 / December 2013

Published online by Cambridge University Press:

15 November 2013, pp. 569-600

Print publication:

December 2013
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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).