Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitesimal dilogarithm on curves over truncated polynomial rings   Let $C$ be a smooth and projective curve over the truncated polynomial ring
$k_m:=k[t]/(t^m), $ where $k$ is a field of characteristic 0. Using a candidate
for the motivic cohomology group ${\rm H}^{3}_{\pazocal{M}}(C,\mathbb{Q}(3))$
based on the Bloch complex of weight 3, we construct regulators to $k$ for
every $m<r<2m.$ Specializing this construction, we obtain an invariant
$\rho_{m,r}(f \wedge g \wedge h)$ of rational functions $f,$ $g$ and $h$ on
$C.$ The current work is a twofold generalization of our work on the
infinitesimal Chow dilogarithm: we sheafify the previous construction and
therefore do not restrict ourselves to triples of rational functions and we
construct the regulator for any $m<r<2m,$ rather than only for $m=2.$ We also
define regulators of cycles, which we expect to give a complete set of
invariants for the infinitesimal part of ${\rm CH}^{2}(k_{m},3). $ This
generalizes Park's work, where the additive Chow cycles, namely the case of
cycles close to 0, is handled for $r=m+1.$ In this paper, we generalize the
reciprocity theorem to pairs of cycles which are the same modulo $(t^m)$ and
for any $m<r<2m.$ We expect the theory of the paper to give regulators on
categories of motives over rings with nilpotents.

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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph