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arXiv · 2510.20138

The abelian fundamental group with modulus in mixed characteristic

Ryosuke Ooe
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Abstract

We define the abelian fundamental group with modulus of a regular flat scheme over a discrete valuation ring, taking into account wild ramification along a divisor. Our definition provides a mixed-characteristic analogue of the abelian fundamental group with modulus introduced by Kerz--Saito for smooth schemes over a perfect field. In this setting, we prove a Lefschetz-type theorem for strictly semi-stable schemes: restriction to a hypersurface of sufficiently large degree relative to the ramification induces an isomorphism of the abelian fundamental groups.

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Ryosuke Ooe. 2025-10-23. The abelian fundamental group with modulus in mixed characteristic. https://arxiv.org/abs/2510.20138

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