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 in [BV12].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.