Descent for l-Adic Polylogarithms

Abstract

AbstractLet L be a finite Galois extension of a number field K. Let G:= Gal(L/K). Let z1,…, zN ∊ L* \ {1} and let m1 …, mN ∊ ℚl. Let us assume that the linear combination of l-adic polylogarithms (constructed in some given way) is a cocycle on GL and that the formal sum is G-invariant. Then we show that cn determines a unique cocycle sn on GK. We also prove a weak version of Zagier conjecture for l-adic dilogarithm. Finally we show that if c2 is “motivic” (m1,…, mN ∊ ℚ) then s2 is also “motivic”.