A Candidate for the Abelian Category of Mixed Elliptic Motives

作者：Patashnick Owen^*

来源：Journal of K-Theory, 2013, 12(3): 569-600.

DOI：10.1017/is013007012jkt237

• arithmetic geometry
• cohomology
• algebraic cycles
• K-theory
• motive
• Lie algebras and their representations
• elliptic curves
• elliptic polylogarithm
• L-function

In this work, 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) .

• 出版日期2013-12