Equivariant Picard groups and Laurent polynomials

Vivek Sadhu

Vol. 312 (2021), No. 1, 219–232

DOI: 10.2140/pjm.2021.312.219

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 $H_{et}^1\left(G;Spec\left(A\right),\mathbb{Z}\right)$. 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