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Multiple Dedekind zeta values are periods of mixed Tate motives

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Horozov,  Ivan
Max Planck Institute for Mathematics, Max Planck Society;

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arXiv:1612.03693.pdf
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Citation

Horozov, I. (2020). Multiple Dedekind zeta values are periods of mixed Tate motives. In R. Donagi, & T. Shaska (Eds.), Integrable systems and algebraic geometry: a celebration of Emma Previato's 65th birthday. Volume 2 (pp. 485-498). Cambridge: Cambridge University Press.


Cite as: https://hdl.handle.net/21.11116/0000-0006-BB61-A
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.