Fζ-geometry, Tate Motives, and the Habiro Ring Catharine Wing Kwan Lo and Matilde Marcolli
نویسنده
چکیده
In this paper we propose different notions of Fζ-geometry, for ζ a root of unity, generalizing notions of F1-geometry (geometry over the “field with one element”) based on the behavior of the counting functions of points over finite fields, the Grothendieck class, and the notion of torification. We relate Fζ-geometry to formal roots of Tate motives, and to functions in the Habiro ring, seen as counting functions of certain ind-varieties. We investigate the existence of Fζ-structures on examples arising from general linear groups, matrix equations over finite fields, and some examples of quantum modular forms.
منابع مشابه
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