Spaces with 𝔾_{𝕞}-action, hyperbolic localization and nearby cycles

Richarz, Timo

doi:10.1090/jag/710

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

Author: Timo Richarz
Journal: J. Algebraic Geom. 28 (2019), 251-289
DOI: https://doi.org/10.1090/jag/710
Published electronically: October 10, 2018
MathSciNet review: 3912059
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Abstract | References | Additional Information

Abstract: We study families of algebraic spaces with ${\mathbb G}_m$-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.

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Additional Information

Timo Richarz
Affiliation: Faculty of Mathematics, University of Duisburg-Essen, Thea-Leymann-Str. 9, 45127 Essen, Germany
MR Author ID: 1004551
Email: timo.richarz@uni-due.de

Received by editor(s): January 19, 2017
Published electronically: October 10, 2018
Additional Notes: This work was finished while the author was supported by the Max-Planck-Institut für Mathematik in Bonn. He cordially thanks everyone for their hospitality and the excellent working conditions.
Article copyright: © Copyright 2018 University Press, Inc.