m at h . A G ] 1 6 Ju n 19 99 THE STEINBERG CURVE HÉLÈNE

Let E and E ′ be elliptic curves over C, with Tate parametrizations p : C ′) sending u ⊗ v to the class of the zero cycle (x, y) − (x, 0) − (0, y) + (0, 0), where x = p(u), y = p ′ (v). We show that, for general u ∈ C * , p * p ′ (u ⊗ (1 − u)) is not zero in CH 2. We also show that the cycle p * p ′ (u ⊗ (1 − u)) is not detectable by a certain class of cohomology theories, including the cohomology of the analytic motivic complex involving the diloga-rithm function defined by S. Bloch in [3]. This is in contrast to itsétale version defined by S. Lichtenbaum [8], which contains the Chow group. 1. Tate curves and line bundles For a scheme X over C, we let X an denote the set of C-points with the classical topology. We let O Xan denote the sheaf of holomorphic functions on X an. We begin by describing a construction of the universal analytic Tate curve over C. We first form the analytic manifoldˆC * as the quotient of the disjoint union ⊔