### Elliptic modular units, by Joerg Wildeshaus

See preprint 0078 for current version. Given an elliptic curve E -----> B over a base B with zero section i, we denote, letting E' := E - i(B), by L(E) the Q-vector space with basis ({s}, s \in E'(B)). Assume that B is smooth and separated over a field of characteristic 0. On the lowest step, the weak version of the elliptic Zagier conjecture predicts the existence of a homo- morphism \phi from the kernel of a certain differential d on L(E) to the vector space O*(B) \otimes Q of units on B. This homomorphism should behave functorially with respect to change of the base B, and it should satisfy a certain norm compatibility. Also, if B is the spectrum of a local field, then the absolute value of \phi should be expressible in terms of the local Neron height function. In this paper, we give a proof of this. We also connect the values of \phi on specific elements of ker(d) to modular, and to elliptic units.

Joerg Wildeshaus <wildesh@math.uni-muenster.de>