2016/12/12 by Ivan Horozov, Horozov, Ivan
Mathematics · #11M32 #11R42 #14G10 #14J40 #32J25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11M32 #msc:11R42 #msc:14G10 #msc:14J40 #msc:32J25
paper · pdf · doi:10.48550/arxiv.1612.03693
In the current draft, the draft is stronger. For instance, the values are mixed Tate periods, not just periods. Also, there is a relation to the moduli spaces of curves of genus zero with marked points. arXiv admin note: text overlap with arXiv:1611.01011
arxiv created 2018/11/20 · arxiv updated 2018/11/21
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.