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arXiv · 2407.10392

Real regulator maps with finite 0-locus

RJ Acuna·Devin Akman·Matt Kerr
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Abstract

A Laurent polynomial in two variables is tempered if its edge polynomials are cyclotomic. Variation of coefficients leads to a family of smooth complete genus $g$ curves carrying a canonical algebraic $K_2$-class over a $g$-dimensional base $S$, hence to an extension of admissible variations of MHS (or normal function) on $S$. We prove that the $\mathbb{R}$-split locus of this extension is finite. Consequently, the torsion locus of the normal function and the $A$-polynomial locus for the family of curves are also finite.

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RJ Acuna, Devin Akman, Matt Kerr. 2024-07-15. Real regulator maps with finite 0-locus. https://arxiv.org/abs/2407.10392

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