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Infinitesimal dilogarithm on curves over truncated polynomial rings

Sinan Ünver

Vol. 18 (2024), No. 4, 685–734
DOI: 10.2140/ant.2024.18.685
Abstract

We construct infinitesimal invariants of thickened one dimensional cycles in three dimensional space, which are the simplest cycles that are not in the Milnor range. This generalizes Park’s work on the regulators of additive cycles. The construction also allows us to prove the infinitesimal version of the strong reciprocity conjecture for thickenings of all orders. Classical analogs of our invariants are based on the dilogarithm function and our invariant could be seen as their infinitesimal version. Despite this analogy, the infinitesimal version cannot be obtained from their classical counterparts through a limiting process.

Keywords
dilogarithm, Bloch group, reciprocity law
Mathematical Subject Classification
Primary: 14C25, 19E15
Milestones
Received: 7 December 2021
Revised: 25 May 2023
Accepted: 3 July 2023
Published: 26 February 2024
Authors
Sinan Ünver
Mathematics Department
Koc University
Istanbul
Turkey

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