Relative DGA and mixed elliptic motives

Kenichiro Kimura; Tomohide Terasoma

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arXiv · 1010.3791

Relative DGA and mixed elliptic motives

Kenichiro Kimura·Tomohide Terasoma

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Abstract

Bloch and Kriz construct an abelian category of mixed Tate motives as the category of comodules over a Hopf algebra obtained by the bar construction of the DGA of cycle complexes. In this paper we generalize their construction to give the definition of a category of mixed elliptic motives, i.e. a Tannakian category of mixed motives generated by an elliptic curve. We introduce the notion of a relative DGA over a reductive group. Then the category of mixed elliptic motives is defined as the category of comodules over the relative bar construction of a certain DGA $A_{EM}$ which is constructed from cycle complexes. The elliptic polylogarithm of Beilinson-Levin gives an interesting object in this category.

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BibTeX RIS

Kenichiro Kimura, Tomohide Terasoma. 2010-10-19. Relative DGA and mixed elliptic motives. https://arxiv.org/abs/1010.3791

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