Spaces with Gm-action, hyperbolic localization and nearby cycles

Richarz, Timo

doi:10.1090/jag/710

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Spaces with G_m-action, hyperbolic localization and nearby cycles

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Richarz, Timo
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/jag/710
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arXiv:1611.01669.pdf
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Richarz, T. (2019). Spaces with G_m-action, hyperbolic localization and nearby cycles. Journal of Algebraic Geometry, 28(2), 251-289. doi:10.1090/jag/710.

Cite as: https://hdl.handle.net/21.11116/0000-0004-8AB9-0

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.