Goncharovʹs relations in Blochʹs higher Chow group CH3(F,5) Original Research Article

In this paper we will prove Goncharovʹs 22-term relations (see [A.B. Goncharov, Geometry of configurations, polylogarithms and motivic cohomology, Adv. Math. 114 (1995) 179–319. [G1]]) in the linearized version of Blochʹs higher Chow group CH3(F,5) using linear fractional cycles of Bloch, Kriz and Totaro under the Beilinson–Soulé vanishing conjecture that CH2(F,n)=0 for ngreater-or-equal, slanted4.