A note on polyhedral cones and toric polylogarithms

Peter Xu

A note on polyhedral cones and toric polylogarithms

K-Theory and Homology 2026-07-01 v1 Algebraic Geometry Number Theory

Authors: Peter Xu

Abstract

We extend some methods of our previous work on special elements in Milnor K-theory of algebraic tori, exhibiting in particular a $\mathrm{GL}_n(\mathbb{Q})$ -equivariant isomorphism between a chain complex of simplicial cones, computing the homology of $S^{n-1}$ , and the trace-fixed part of the weight-n Gersten complex for the Milnor K- theory of $\mathbb{G}_m^n$ over $\mathbb{Q}$ . Via a relationship between graded pieces of algebras of cones and Steinberg modules, this refines a result of Charlton-Radchenko-Rudenko.

Cite

@article{arxiv.2607.01543,
  title  = {A note on polyhedral cones and toric polylogarithms},
  author = {Peter Xu},
  journal= {arXiv preprint arXiv:2607.01543},
  year   = {2026}
}