Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593411 | Journal of Number Theory | 2016 | 51 Pages |
Abstract
We study Galois descents for categories of mixed Tate motives over ON[1/N]ON[1/N], for N∈{2,3,4,8}N∈{2,3,4,8} or ONON for N=6N=6, with ONON the ring of integers of the N th cyclotomic field, and construct families of motivic iterated integrals with prescribed properties. In particular this gives a basis of multiple zeta values via multiple zeta values at roots of unity μNμN. It also gives a new proof, via Goncharov's coproduct, of Deligne's results [9]: the category of mixed Tate motives over OkN[1/N]OkN[1/N], for N∈{2,3,4,8}N∈{2,3,4,8} is spanned by the motivic fundamental groupoid of P1∖{0,μN,∞}P1∖{0,μN,∞} with an explicit basis. By applying the period map, we obtain a generating family for multiple zeta values relative to μNμN.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Claire Glanois,