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arXiv · 1612.03693

Multiple Dedekind Zeta Values are Periods of Mixed Tate Motives

Ivan Horozov
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Abstract

Recently, the author defined multiple Dedekind zeta values [5] associated to a number K field and a cone C. These objects are number theoretic analogues of multiple zeta values. In this paper we prove that every multiple Dedekind zeta value over any number field K is a period of a mixed Tate motive. Moreover, if K is a totally real number field, then we can choose a cone C so that every multiple Dedekind zeta associated to the pair (K;C) is unramified over the ring of algebraic integers in K. In [7], the author proves similar statements in the special case of a real quadratic fields for a particular type of a multiple Dedekind zeta values. The mixed motives are defined over K in terms of a the Deligne-Mumford compactification of the moduli space of curves of genus zero with n marked points.

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Ivan Horozov. 2016-12-12. Multiple Dedekind Zeta Values are Periods of Mixed Tate Motives. https://arxiv.org/abs/1612.03693

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