Title: Relative completion and Beilinson conjecture for Kuga fiber space.
Abstract: We constructed a Hopf algebra (with K. Kimura) associated to the category of mixed elliptic motives. To study relations between typical generators, it is necessary to study regulator map for Eisenstein elements. We prove the Beilinson conjecture for the relation between spcial value of L-function and regulator map for Kuga fiber space. This is a generalization of Beilison's earlier work for modular curves.