Functional equations of the dilogarithm in motivic cohomology |
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Authors: | Oliver Petras |
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Institution: | Fachbereich Physik, Mathematik und Informatik, Johannes Gutenberg - Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany |
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Abstract: | We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm. These relations suffice, as we shall demonstrate with a few examples, to write down enough relations in Bloch's integral higher Chow group CH2(F,3) for certain number fields F to detect torsion cycles. Using the regulator map to Deligne cohomology, one can check the non-triviality of the torsion cycles thus obtained. Using this combination of methods, we obtain explicit higher Chow cycles generating the integral motivic cohomology groups of some number fields. |
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Keywords: | 11G55 11R70 11S70 11F42 |
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