Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Infinitesimal Chow Dilogarithm


Author: Sinan Ünver
Journal: J. Algebraic Geom.
DOI: https://doi.org/10.1090/jag/746
Published electronically: December 16, 2019
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Abstract: Let $ C_{2}$ be a smooth and projective curve over the ring of dual numbers of a field $ k.$ Given non-zero rational functions $ f,g,$ and $ h$ on $ C_{2},$ we define an invariant $ \rho (f\wedge g \wedge h) \in k.$ This is an analog of the real analytic Chow dilogarithm and the extension to non-linear cycles of the additive dilogarithm of [Algebra Number Theory 3 (2009), pp. 1-34]. Using this construction we state and prove an infinitesimal version of the strong reciprocity conjecture of Goncharov [J. Amer. Math. Soc. 18 (2005), pp. 1-60] with an explicit formula for the homotopy map. Also using $ \rho ,$ we define an infinitesimal regulator on algebraic cycles of weight two which generalizes Park's construction in the case of cycles with modulus [Amer. J. Math. 131 (2009), pp. 257-276].


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Sinan Ünver
Affiliation: Department of Mathematics, Koç University, Rumelifeneri Yolu, 34450, Istanbul, Turkey; and Department of Mathematics, Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany
Email: sunver@ku.edu.tr

DOI: https://doi.org/10.1090/jag/746
Received by editor(s): April 10, 2019
Published electronically: December 16, 2019
Article copyright: © Copyright 2019 University Press, Inc.