A Short Proof of a Grothendieck-Lefschetz Theorem for Equivariant Picard Groups

TL;DR

This paper presents a concise proof of a Grothendieck-Lefschetz theorem specifically for equivariant Picard groups of smooth varieties under affine algebraic group actions, simplifying previous approaches.

Contribution

It provides a shorter, more direct proof of a key theorem in algebraic geometry concerning equivariant Picard groups, enhancing understanding and accessibility.

Findings

Short proof of Grothendieck-Lefschetz theorem for equivariant Picard groups

Applicable to nonsingular varieties with affine algebraic group actions

Simplifies existing proofs in algebraic geometry

Abstract

We give a short proof of a Grothendieck-Lefschetz Theorem for equivariant Picard groups of nonsingular varieties with the action of an affine algebraic group.