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. 13, 2018 4:08 PM - Last modified Feb. 13, 2018 4:08 PM