### 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>