Mixed elliptic motives, by Alexander B. Goncharov

We define complexes which hypothetically compute certain pieces of K-theory of powers of elliptic curve E over an arbitrary field k. In particular when k is a number field this leads to a precise conjecture expressing the special values L(Sym^nE,n+1) via the classical Eisenstein-Kronecker series. (This conjecture can be considered as an elliptic analog of Zagier's conjecture; it was also discussed by J. Wildeshaus). We formulate several conjectures about the category of mixed elliptic motives generalizing some conjectures about the mixed Tate motives.

Alexander B. Goncharov <sasha@mpim-bonn.mpg.de>