Brief communications

The Strong Suslin Reciprocity Law and Its Applications to Scissor Congruence Theory in Hyperbolic Space

D. Rudenko

National Research University "Higher School of Economics" (HSE), Moscow

Abstract: We prove the strong Suslin reciprocity law conjectured by A. B. Goncharov and describe its corollaries for the theory of scissor congruence of polyhedra in hyperbolic space. The proof is based on the study of Goncharov's conjectural description of certain rational motivic cohomology groups of a field. Our main result is a homotopy invariance theorem for these groups.

Keywords: scissor congruence, reciprocity laws, motivic cohomology, polylogarithms.

UDC: 512.667.3

Received: 31.07.2015

DOI: 10.4213/faa3229

 English version: Functional Analysis and Its Applications, 2016, 50:1, 66–70

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