Mathematical Research Letters

Volume 11, Issue 6, November 2004 pp. 771-784.

Euclidean scissor congruence groups and mixed Tate motives over dual numbers

Authors: A. B. Goncharov
Author institution: Brown University

Summary: We define Euclidean scissor congruence groups for an arbitrary algebraically closed field $F$ and formulate a conjecture describing them. Using the Euclidean and Non-Euclidean $F$--scissor congruence groups we construct a category which is conjecturally equivalent to a subcategory of the category ${\cal M}_T(F_{\varepsilon})$ of mixed Tate motives over the dual numbers $F_{\varepsilon}:= F[\varepsilon]/\varepsilon^2$.

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