Equivariant Picard groups and Laurent polynomials

Abstract

Let $G$ be a finite group. For a $G$-ring $A,$ let ${\mathrm{Pic}}^G(A)$ denote the equivariant Picard group of $A.$ We show that if $A$ is a finite type algebra over a field $k$ then ${\mathrm{Pic}}^G(A)$ is contracted in the sense of Bass with contraction $H_{et}^1(G;Spec(A),\mathbb{Z}).$ This gives a natural decomposition of the group ${\mathrm{Pic}}^G(A[t,t^{-1}]).$

Final Version, accepted for publication