Euclidean scissor congruence groups and mixed Tate motives over dual numbers

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 $F_{\varepsilon}:= F[\varepsilon]/\varepsilon^2$.

Full Text (PDF format)

Published 1 January 2004