2018/11/18 by Ishai Dan‐Cohen, Dan-Cohen, Ishai, David Corwin +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1811.07364
openalex publication_date 2018/11/18 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
Building on work by Dan-Cohen--Wewers, Dan-Cohen [DC], and Brown, we push the\ncomputational boundary of our explicit motivic version of Kim's method in the\ncase of the thrice punctured line over an open subscheme of Spec ZZ. To do so,\nwe develop a refined version of the algorithm of [DC] tailored specifically to\nthis case. We also commit ourselves fully to working with the polylogarithmic\nquotient. This allows us to restrict our calculus with motivic iterated\nintegrals to the so-called depth-one part of the mixed Tate Galois group\nstudied extensively by Goncharov. An application was given in part one, where\nwe verified Kim's conjecture in an interesting new case.\n