Geodesic
The Strong Suslin Reciprocity Law and Its Applications to Scissor Congruence Theory in Hyperbolic Space
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 79-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : polylogarithms. 
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D. Rudenko. The Strong Suslin Reciprocity Law and Its Applications to Scissor Congruence Theory in Hyperbolic Space. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 79-84. http://geodesic.mathdoc.fr/item/FAA_2016_50_1_a7/

[1] A. A. Beilinson, P. Deligne, Motives, Proc. Symp. Pure Math., 55, part 2, Amer. Math. Soc., Providence, RI, 1994, 97–121 | DOI | MR | Zbl

[2] J. L. Dupont, Osaka J. Math., 19:3 (1982), 599–641 | MR

[3] A. B. Goncharov, J. Amer. Math. Soc., 18:1 (2005), 1–60 | DOI | MR | Zbl

[4] A. B. Goncharov, Proc. Sympos. Pure Math., 55, part 2, Amer. Math. Soc., Providence, RI, 1994, 43–96 | DOI | MR | Zbl

[5] A. Suslin, V. Voevodsky, The Arithmetic and Geometry of Algebraic Cycles (Banff, AB, 1998), NATO Sci. Ser. C Math. Phys. Sci., 548, Kluwer Acad. Publ., Dordrecht, 2000, 117–189 | MR | Zbl

[6] A. A. Suslin, Izv. AN SSSR, ser. matem., 43:6 (1979), 1394–1429 | MR | Zbl

[7] A. A. Suslin, Teoriya Galua, koltsa, algebraicheskie gruppy i ikh prilozheniya, Trudy MIAN, 183, Nauka, Leningradskoe otd., L., 1990, 180–199 | MR