m at h . A G ] 7 N ov 2 00 3 Goncharov ’ s Relations in Bloch ’ s higher Chow Group CH 3 ( F , 5 ) ∗
نویسنده
چکیده
where Gn, denoted by Bn by Goncharov, is placed at degree 1. To save space we here only point out that Gn(F ) are quotient groups of Z[P 1 F ] and refer the interested readers to [G2, p.49] for the detailed definition of these groups. On the other hand, currently there are two versions of higher Chow groups available: simplicial and cubical, which are isomorphic (cf. [Le]). We will recall the cubical version in §2 and use it throughout this paper. Define the Z-linear map β2 : Z[P 1 F ] −→ ∧2 F by β2({x}) = (1 − x) ∧ x for x 6= 0, 1 and β2({x}) = 0 for x = 0, 1. Let B2(F ) be the Bloch group defined as the quotient group of ker(β2) by the 5-term relations satisfied by the dilogarithm. In [GM] Gangl and Müller-Stach prove that there is a well-defined map to the higher Chow group
منابع مشابه
Goncharov ’ s relations in Bloch ’ s higher Chow group CH 3 ( F , 5 ) ✩
In this paper we will prove Goncharov’s 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 Bloch’s 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 n 4. © 2006 Elsevier In...
متن کاملN ov 2 00 3 Supplement to : Goncharov ’ s Relations in Bloch ’ s higher Chow
In this supplement we prove the admissibility of all the cycles appearing in the paper Goncharov’s Relations in Bloch’s higher Chow Group CH3(F, 5). First let’s recall the following two Lemmas: Lemma 3.1. (Gangl-Müller-Stach) Let fi (i = 1, 2, 3, 5) be rational functions and f4(x, y) be a product of fractional linear transformations of the form (a1x+b1y+c1)/(a2x+b2y+c2). We assume that all the ...
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