q-deformations of statistical mechanical systems and motives over finite fields
Mathematical Physics
2017-04-24 v1 math.MP
Abstract
We consider q-deformations of Witt rings, based on geometric operations on zeta functions of motives over finite fields, and we use these deformations to construct q-analogs of the Bost-Connes quantum statistical mechanical system. We show that the q-deformations obtained in this way can be related to Habiro ring constructions of analytic functions over the field with one element and to categorifications of Bost-Connes systems.
Keywords
Cite
@article{arxiv.1704.06367,
title = {q-deformations of statistical mechanical systems and motives over finite fields},
author = {Matilde Marcolli and Zhi Ren},
journal= {arXiv preprint arXiv:1704.06367},
year = {2017}
}
Comments
25 pages, LaTeX