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Title: The polylog quotient and the Goncharov quotient in computational Chabauty–Kim Theory I
Polylogarithms are those multiple polylogarithms that factor through a certain quotient of the de Rham fundamental group of the thrice punctured line known as the polylogarithmic quotient. Building on work of Dan-Cohen, Wewers, and Brown, we push the computational boundary of our explicit motivic version of Kim’s method in the case of the thrice punctured line over an open subscheme of [Formula: see text]. To do so, we develop a greatly refined version of the algorithm of Dan-Cohen tailored specifically to this case, and we focus attention on the polylogarithmic quotient. This allows us to restrict our calculus with motivic iterated integrals to the so-called depth-one part of the mixed Tate Galois group studied extensively by Goncharov. We also discover an interesting consequence of the symmetry-breaking nature of the polylog quotient that forces us to symmetrize our polylogarithmic version of Kim’s conjecture. In this first part of a two-part series, we focus on a specific example, which allows us to verify an interesting new case of Kim’s conjecture.  more » « less
Award ID(s):
1646385
PAR ID:
10231956
Author(s) / Creator(s):
;
Date Published:
Journal Name:
International Journal of Number Theory
Volume:
16
Issue:
08
ISSN:
1793-0421
Page Range / eLocation ID:
1859 to 1905
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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