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 Adv. Math. (231 (2012) 1327-1363). 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.
Infinite root stacks and quasi-coherent sheaves on logarithmic schemes
Talpo, Mattia;Vistoli, Angelo
2018
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 Adv. Math. (231 (2012) 1327-1363). 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.File in questo prodotto:
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Talpo_et_al-2018-Proceedings_of_the_London_Mathematical_Society.pdf
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