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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Infinitesimal Chow dilogarithm

Author: Si̇nan Ünver
Journal: J. Algebraic Geom. 30 (2021), 529-571
Published electronically: December 16, 2019
MathSciNet review: 4283551
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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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Si̇nan Ünver
Affiliation: Department of Mathematics, Koç University, Rumelifeneri Yolu, 34450, Istanbul, Turkey; and Department of Mathematics, Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany

Received by editor(s): April 10, 2019
Published electronically: December 16, 2019
Article copyright: © Copyright 2019 University Press, Inc.