Spaces with ${\mathbb{G}}_m$-action, hyperbolic localization and nearby cycles

Abstract

We study families of algebraic spaces with a fiberwise ${\mathbb{G}}_m$-action and prove Braden's theorem on hyperbolic localization for arbitrary base schemes. As an application, we obtain that hyperbolic localization commutes with nearby cycles.

Typos corrected, references added

References in corpus (1)

• A Luna étale slice theorem for algebraic stacks