Tangent to Bloch-Suslin and Grassmannian Complexes over the dual numbers

Abstract

In this article, we extend Siegel's cross-ratio identity for $2\times 2$ determinants over the truncated polynomial ring $F[\epsilon {]}_{\nu }:=F[\epsilon ]/{\epsilon }^{\nu }$. We compute cross-ratios and Goncharov's triple-ratios in $F[\epsilon {]}_2$ and $F[\epsilon {]}_3$ and use them extensively in our computations for the tangential complexes. We also verify a "projected five-term" relation in the group $T{\mathcal{B}}_2(F)$ which is crucial to prove one of our central statements that describe the morphisms between tangent complex and Grassmannian complex

24 pages

References in corpus (1)

• Configuration complexes and a variant of Cathelineau's complex in weight 3