Euclidean scissor congruence groups and mixed Tate motives over dual numbers
نویسنده
چکیده
We define Euclidean scissor congruence groups for an arbitrary algebraically closed field F and formulate a conjecture describing them. Using the Euclidean and NonEuclidean F–scissor congruence groups we construct a category which is conjecturally equivalent to a subcategory of the category MT (Fε) of mixed Tate motives over the dual numbers Fε := F [ε]/ε . 1. Euclidean scissor congruence groups and a generalization of Hilbert’s third problem. Let F be an arbitrary algebraically closed field. In Chapter 3 of [8] we defined an F–scissor congruence group Sn(F ) of polyhedrons in the projective space P (F ) equipped with a non-degenerate quadric Q. The classical spherical and hyperbolic scissor congruence groups are subgroups of Sn(C). The direct sum S•(F ) := ⊕n≥0Sn(F ); S0(F ) = Q
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