#### Vol. 312, No. 1, 2021

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Equivariant Picard groups and Laurent polynomials

Vol. 312 (2021), No. 1, 219–232
##### Abstract

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

##### Keywords
equivariant Picard groups, contracted functor, G-sheaves
##### Mathematical Subject Classification
Primary: 14C35
Secondary: 19E08, 18E10
##### Milestones
Received: 6 October 2020
Revised: 4 February 2021
Accepted: 22 March 2021
Published: 4 August 2021
##### Authors
 Vivek Sadhu Indian Institute of Science Education and Research Bhopal Bhopal India