Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose that $X$ is a variety (in char 0) with an action of an affine algebraic group $G$. Let $Y \subset X$ be a subvariety fixed by $G$--the action map agrees with projection upon restriction to $Y$. Let $\widehat{Y}$ be the formal completion of $X$ along $Y$. Furthermore let $\widehat{G}$ be the the completion of $G$ at the identity, viewed as a formal group. There is a restriction functor $j^*$ from the $Qcoh^G(X)$, the category of $G$-equivariant quasicoherent sheaves on $X$, to $Qcoh^{\widehat{G}}(\widehat{Y})$, the category of $\widehat{G}$-equivariant quasicoherent sheaves on $\widehat{Y}$.

1) Is this situation considered in the literature? Where?
2) What tools are available to control this functor? How might one describe the essential image?

Although curious about this general package, I specifically care about the case $G =\mathbb{G}_m$.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.