Charanya Ravi: A Grothendieck-Lefschetz theorem for equivariant Picard groups

Let G be a finite (abstract) group and let k be a field of characteristic zero. We prove that for a non-singular projective G-variety X over k, and a non-singular G-invariant subvariety Y of dimension >= 3, which is a scheme-theoretic complete intersection in X, the pullback map PicG(X) -> PicG(Y) is an isomorphism. This is an equivariant analog of the Grothendieck-Lefschetz theorem for Picard groups.

Published Feb. 20, 2018 6:19 PM - Last modified Feb. 20, 2018 6:19 PM