- CiteKey: “Gon95” - Type: journalArticle - Title: “Geometry of Configurations, Polylogarithms, and Motivic Cohomology,” - Author: “Goncharov, A. B.;” - Year: 1995 - DOI: 10.1006/aima.1995.1045 - Collections: “Syllabus; Talbot 2022,”

Geometry of Configurations, Polylogarithms, and Motivic Cohomology

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• URL: https://www.sciencedirect.com/science/article/pii/S0001870885710456
• URI: http://zotero.org/users/1049732/items/LC6IIRYL
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Abstract

Let A be a discrete valuation ring with field of fractions F and residue field k such that |k|≠2,3,4,5,7,8,9,16,27,32,64$$|k|≠2,3,4,5,7,8,9,16,27,32,64. We prove that there is a natural exact sequence where RP1(k)$$RP1(k) is the refined scissors congruence group of k. Let Γ0(mA)$$Γ0(mA) denote the congruence subgroup consisting of matrices in SL2(A)$$SL2(A) whose lower off-diagonal entry lies in the maximal ideal mA$$mA. We also prove that there is an exact sequence where I2(k)$$I2(k) is the second power of the fundamental ideal of the Grothendieck-Witt ring GW(k)$$GW(k) and P‾(k)$$P‾(k) is a certain quotient of the scissors congruence group (in the sense of Dupont-Sah) P(k)$$P(k) of k. For an infinite field F, we study the kernel of the map and the cokernel of We give conjectural estimates of these kernels and cokernels and prove our conjectures for n≤4$$n≤4.

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