An analogue of cyclotomic units for products of elliptic curves

Details An analogue of cyclotomic units for products of elliptic curves An analogue of cyclotomic units for products of elliptic curves

2001-10-17

arxiv.org/abs/math/0110180v2

Mathematics

Number Theory

25 pages. Typos and a statement of a theorem of Scholl and Harris corrected

Scientific paper

We construct certain elements in the integral motivic cohomology group $H^3_{{\cal M}}(E \times E',\Q(2))_{\ZZ}$, where $E$ and $E'$ are elliptic curves over $\Q$. When $E$ is not isogenous to $E'$ these elements are analogous to `cyclotomic units' in real quadratic fields as they come from modular parametrisations of the elliptic curves. We then find an analogue of the class number formula for real quadratic fields. Finally we use the Beilinson conjectures for $E \times E'$ to deduce them for products of $n$ elliptic curves. A certain amount of this paper is expository in nature.

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