A Candidate for the abelian category of mixed elliptic motives

2010/10/22 by Owen Patashnick, Patashnick, Owen · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #math.AG #math.KT #math.NT

paper · pdf · doi:10.48550/arxiv.1010.4685

2 figures

arxiv created 2013/07/03 · arxiv updated 2013/07/04

Abstract

In this paper we suggest a definition 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-Soule 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). This paper was essentially written in the late 1990's whilst the author was at the University of Chicago. The author apologizes for the tardiness of this posting, and hopes the reader will still find the content interesting.

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