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1 results

  • 15 - Multiple Dedekind Zeta Values are Periods of Mixed Tate Motives

  • Edited by Ron Donagi, University of Pennsylvania, Tony Shaska, Oakland University, Michigan
  • Book:
    Integrable Systems and Algebraic Geometry
    Published online:
    19 March 2020
    Print publication:
    02 March 2020, pp 485-498

  • Summary

    Recently, the author defined multiple Dedekind zeta values 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 his related book, the author proves similar statements in the special case of real quadraticfields for a particular type of multiple Dedekind zeta values. The mixed motives are defined over K in terms of the Deligne–Mumford compactification of the moduli space of curves of genus zero with n marked points.