ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 14, 19, 33 Gangl, Herbert, Institute for Experimental Mathematics, Essen, Germany, Mueller-Stach, Stefan, Universität Essen, Germany Polylogarithmic identities in cubical higher Chow groups The algebraic K-groups K_{2m−1}^{(m)}(F)_{ℚ} (tensored with ℚ) of a field F are known to be isomorphic to Bloch’s higher Chow groups CH^{m}(F, 2m − 1)_{ℚ} and conjectured to be isomorphic to the Bloch groups B_{m}(F)_{ℚ} of Bloch (m = 2) and Zagier (m > 2). For m = 2 we realize the isomorphism B_{2}(F)_{ℚ} → CH^{2}(F, 3)_{ℚ} by proving Abel’s 5-term relation for the dilogarithm in CH^{2}(F, 3)_{ℚ} among certain distinguished cycles given by Totaro. We also shed some light on the relation between B_{3}(F)_{ℚ} and CH^{3}(F, 5)_{ℚ} by proving further identities corresponding to functional equations of the trilogarithm.