Infinite root stacks and quasi-coherent sheaves on logarithmic schemes

Abstract

We define and study infinite root stacks of fine and saturated logarithmic schemes, a limit version of the root stacks introduced by Niels Borne and the second author. We show in particular that the infinite root stack determines the logarithmic structure, and recovers the Kummer-flat topos of the logarithmic scheme. We also extend the correspondence between parabolic sheaves and quasi-coherent sheaves on root stacks to this new setting.

v2: 61 pages. Final version, to appear in Proc. Lond. Math. Soc

References in corpus (3)

• Parabolic sheaves on logarithmic schemes
• Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes
• Derived Logarithmic Geometry I

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• G-theory of root stacks and equivariant K-theory
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