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log geometry

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

KUMMER COVERINGS AND SPECIALISATION
Part of
- Algebraic geometry: Foundations
- Families, fibrations
Martin Olsson
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 21 / Issue 3 / May 2022

Published online by Cambridge University Press:

01 March 2021, pp. 1029-1065

Print publication:

May 2022
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We prove versions of various classical results on specialisation of fundamental groups in the context of log schemes in the sense of Fontaine and Illusie, generalising earlier results of Hoshi, Lepage and Orgogozo. The key technical result relates the category of finite Kummer étale covers of an fs log scheme over a complete Noetherian local ring to the Kummer étale coverings of its reduction.